Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Unit 3:
Data Analysis
and Probability
Lesson Topics:
Lesson 1:
Lesson 2:
Lesson 3:
Lesson 4:
Lesson 5:
Lesson 6:
Lesson 7:
Lesson 8:
Lesson 9:
Types of Graphs (PH text p.796-800)
Frequency and Histograms (PH text 12.2)
Measures of Central Tendency and Dispersion (PH text 12.3)
Stem and Leaf Plots (PH text p.800)
Box-and-Whisker Plots (PH text 12.4)
Scatterplots/Scattergrams (PH text 5.7)
Permutations and Combinations (PH text 12.6) - optional
Theoretical and Experimental Probability (PH text 12.7)
Probability of Compound Events (PH text 12.8)
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Lesson 1: Types of Graphs (not in PH text)
Objective: To identify, interpret and choose between different types of graphs
Types of Graphs:
Histogram – a special type of bar graph used to show frequencies – there is one bar for each
interval – there are no gaps between bars, and all bars are of equal width
– most appropriate to visually compare frequencies at which specific data items (or groups)
occur
Stem and Leaf Plot – most appropriate to display the individual data items in an ordered and
concise manner
Box-and-Whisker Plot – used to show the general layout of a set of data, where most of the
numbers fall
– most appropriate to display the median, lower and upper quartiles, and least and greatest
values, AND/OR to compare these aspects of multiple sets of data
Scatterplot/Scattergram – a display of unconnected points that show the relationship between
two sets of data
– most appropriate to display the correlation (relationship) between two sets of data
Bar Graph – a graph that is created using bars to fill the space from the axis to the data point
– most often, one axis has the quantity while the other axis has the categories being compared
– most appropriate to compare numbers or amounts of items
Line Graph – a graph that shows information that is connected in some way; a graph that is
created using line segments to connect data points
– most appropriate to show how a set of data changes over time
Circle (or Pie) Graph – used to represent data as parts of a whole – entire circle represents the
whole, or 100%, of the data – each wedge/sector represents a part of the data – the central
angles must be proportionate to the percent of the whole it represents (a whole circle contains 360o)
– most appropriate to visually represent the parts of a set of data to the whole for comparison
(percents)
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Types of Data:
Continuous Data -
Best choice for a graph of something that
continues without breaks is _____________
Discrete Data -
Best choice for a graph of something that has a
specific number of data points, or a count of
something is ____________________
Pie charts are good for showing a comparison of
percentages using discrete data.
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
HW: p. 796-799 (total of 11 questions on all pages)
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Lesson 2: Frequency and Histograms (PH text 12.2)
Objective: to make and interpret frequency tables and histograms
Frequency Distribution/Table - A method of organizing a set of data into intervals to show how often an
item in each interval occurs
Frequency – the number of data values in that interval
Make a frequency distribution from the data below.
Hours worked:
5, 6, 6, 5, 7, 8, 6, 5, 7, 5, 5, 6, 6, 8, 5, 6, 8, 6
hours worked
tally
frequency
5
6
7
8
Frequency Table with Intervals A frequency table that has the data grouped in equal intervals
Make a frequency table and histogram with intervals for the data below.
Ages of Company Presidents
45
58
60
62
56
58
55
48
39
50
65
48
50
42
60
38
55
47
39
35
44
74
Frequency Table
Tally
Frequency
Frequency (# of people)
Age Group
Histogram
30-39
40-49
50-59
60-69
70-79
30-39
40-49
50-59
Age Groups
9
60-69
70-79
Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Histogram – a graph that displays data from a frequency table – has one bar for each interval – there are
no gaps between bars, and all bars are of equal width
HW: p.723 #8-10 (make BOTH a frequency table and a histogram), 14-17, 22-31, 34-35
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Lesson 3: Measures of Central Tendency and Dispersion (PH text 12.3)
Objective: to find mean, median, mode and range of a set of numbers
Measures of Central Tendency:
Mean – the "average" you're used to, where you add up all the numbers and then divide by the number of
numbers. – or, the sum of n numbers divided by n -- the symbol for mean is x
Median – the "middle" value in the list of numbers - To find the median, your numbers have to be listed in
numerical order, so you may have to rewrite your list first.
Mode – the value that occurs most often (If no number is repeated, then there is no mode for the list.)
Range – the difference between the largest and smallest values – this is a measure of dispersion, NOT a
measure of central tendency, but frequently useful information when describing a set of data
Example: Find the mean, median, mode and range for this set of data. These are the daily salaries of seven
people who work for the same company.
$120 $98
$134
$458
$122
$128
$125
Mean: _____________
Median: _____________
Mode: _____________
Range: _____________
Outlier – a data value that is significantly higher or lower than the other values in the set of numbers
Look at the set of data above. Would you consider any of those values to be an outlier?
Choosing a measure of central tendency:
Sometimes, one (or more than one) measure of central tendency is a better descriptor of a set of data.
Mean – good when there are no outliers, or extreme values
Median – best choice when there are outliers, or extreme values
Mode – only use for non-numeric data, or when choosing the most popular item
Range – never a good measure of central tendency, but the range does show how closely grouped the set of
data is
Example: Use the data above. Which measure of central tendency best describes the data? Why?
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Measures of Central Tendency Practice:
Directions: Find the measures of central tendency. Which best describes the data?
Explain why.
1)
The number of students in NP elementary schools:
597 581
555
384
463
620
407
656
426
Mean:
407
547
566
_____________
Median: _____________
Mode:
_____________
Best measure(s) of central tendency:
Explanation:
2)
The current prices per share (in $) of twelve stocks:
59
97
53
83
45
47
88
47
51
Mean:
47
62
47
_____________
Median: _____________
Mode:
_____________
Best measure(s) of central tendency:
Explanation:
3)
The prices (in $) of Edmund’s video games:
60
57
84
15
59
63
60
67
59
Mean:
75
72
_____________
Median: _____________
Mode:
Best measure(s) of central tendency:
Explanation:
13
_____________
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Finding a data value when you know the mean:
Sometimes you will be given the mean of a set of data along with some of the individual values, and be
asked to find the remaining data value. In this case, you write an equation using a variable to represent the
missing value. Then solve the equation to find the value.
Example:
Kayla has sales of $1280, $1125, $965, and $1210 the first four days of the week. How much does she need
to sell on the fifth day to average $1150 for the week?
The swim team wants an average of 40 laps for the day’s training session. If the other swimmers do 35, 26,
47, 40, 45, 50, 31, and 46 laps, how many laps does Char need to do to ensure the average of 40 laps is met?
Practice:
HW: p.730 #5, 6-18 even, 28-29
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Lesson 4: Stem and Leaf Plots (PH text p.800)
Objective: to read, use and create stem and leaf plots
Stem and Leaf Plot A method of displaying data so that the frequency is easily seen, yet the value of each number is maintained
leaf – the last digit on the right of a given number
stem – the digit(s) remaining when the leaf digit is dropped
Stem-and-Leaf Plots (from PurpleMath.com)
Stem-and-leaf plots are a method for showing the frequency with which certain classes of values occur. You could
make a frequency distribution table or a histogram for the values, or you can use a stem-and-leaf plot and let the
numbers themselves to show pretty much the same information.
For instance, suppose you have the following list of values: 12, 13, 21, 27, 33, 34, 35, 37, 40, 40,
make a frequency distribution table showing how many tens, twenties, thirties, and forties you have:
Frequency
Class
Frequency
10 - 19
2
20 - 29
2
30 - 39
4
40 - 49
3
41. You could
You could make a histogram, which is a bar-graph showing the number of occurrences, with the classes being
numbers in the tens, twenties, thirties, and forties:
(The shading of the bars in a histogram isn't necessary, but it can be helpful by making the bars easier to see,
especially if you can't use color to differentiate the bars.)
The downside of frequency distribution tables and histograms is that, while the frequency of each class is easy to see,
the original data points have been lost. You can tell, for instance, that there must have been three listed values that
were in the forties, but there is no way to tell from the table or from the histogram what those values might have been.
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
On the other hand, you could make a stem-and-leaf plot for the same data:
The "stem" is the left-hand column which contains the tens digits. The "leaves" are the lists in the right-hand column,
showing all the ones digits for each of the tens, twenties, thirties, and forties. As you can see, the original values can
still be determined; you can tell, from that bottom leaf, that the three values in the forties were 40, 40, and 41.
Note that the horizontal leaves in the stem-and-leaf plot correspond to the vertical bars in the histogram, and
the leaves have lengths that equal the numbers in the frequency table.
Make a stem and leaf plot for the data below.
Ages of Company Presidents
45
58
60
62
56
58
55
48
39
50
65
48
50
42
60
38
55
47
39
35
44
74
Ages of Company Presidents
(Stems)
(Leaves)
3
4
5
6
7
Find the mean, median, mode and range for this set of data. Does the stem-and-leaf plot make this process
any easier? Why?
Mean:
Median:
Mode:
Range:
Look at www.purplemath.com stem-and-leaf examples.
HW: Stem and Leaf Practice page; p.731 # 31; p.800 #1-5
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Less
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Lesson 5: Box-and-Whisker Plots (PH text 12.4)
Objective: To make and interpret box-and-whisker plots and to find and interpret quartiles
A box-and-whisker plot is used to show the general layout of a set of data – where most of the numbers fall.
It shows the median of the whole set, the median of both halves, and the highest and lowest numbers in the
data set.
Quartile: values that divide a set of data into four equal parts.
Data is divided into four parts, or quartiles. The median (Q2) of the entire set of numbers is the center of the
“box.” The numbers less than the median are then divided into two sections by finding the median of those
numbers. That new median is called the first (or lower) quartile (Q1), and is the marker for the left side of
the box. Finding the median of the values greater than the original median gives you the third (or upper)
quartile value (Q3); this is the marker for the right side of the box. The lowest value is the end of the left
whisker, and the highest value is the end of the right whisker.
Example:
18, 27, 34, 52, 54, 59, 61, 68, 78, 82, 85, 87, 91, 93, 100
↑
↑
↑
First
Median
Third
Quartile
(Q2)
Quartile
(Q1)
(Q3)
To graph this data, we create a number line including at least all of the values in the set of data. The boxand-whisker plot is placed on or near the number line as indicated above.
Least
Value
First
Quartile
Third
Quartile Greatest
Value
Median
When multiple sets of data are plotted together, a box-and-whisker plot is an easy way to make a quick
visual comparison of sets of data.
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Box-and-Whisker Plot Practice
Use this box-and-whisker plot to answer #1-4.
1. What is the age of the oldest dog(s) in the show? ____________
2. What is the median age of the dogs? ____________
3. What number is in the lower quartile? ____________
4. About what fraction of the dogs are 5 years old or older? ____________
Use this box-and-whisker plot to answer #5-8.
5. What is the median of all the scores? ____________
6. What number is in the lower quartile? ____________
7. What part of the data is in the box (between 70 and 80)?
a. The top one-fourth of the scores
b. The middle half of the scores
c. The lower half of the scores
d. The lowest fourth of the scores
8. Which statement best describes the scores?
a. They are spread evenly from 65 to 95.
b. There are more scores in the upper fourth than in the lower fourth of the scores.
c. The scores are bunched closer together in the lowest ¼ of the scores than in the highest ¼.
d. The mean of the scores is 70.
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Box-and-Whisker Plot Practice (cont.)
9.
This box-and-whisker plot shows the amount of money raised by 11 volunteers in a charity walk.
a. About how many people raised less than $56? ____________
b. Use what you know about box-and-whisker plots to explain why your answer is correct. Use
words and/or numbers in your explanation.
Create a box-and-whisker plot for each set of data.
10.
{65, 66, 59, 61, 67, 70, 67, 66, 69, 70, 63}
11.
{1, 1.5, 1.7, 2, 6.1, 6.2, 7}
HW: p.738 #14-16, 20, 24, 27, 28, 30
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Lesson 6: Scatterplots/Scattergrams and Line Graphs (PH text 5.7)
Objectives:
to draw, interpret, and analyze trends in scatter plots and line graphs
Introduction
Line graphs provide an excellent way to map independent and dependent variables that are both quantitative
(measured with numbers). Scatter plots are similar to line graphs in that they start with plotting quantitative
data points. The difference is that with a scatter plot, we do not connect individual points. In the scatter plot
we just look at the trend, which can be represented with a trend line.
Both scatter plots and line graphs will have one independent and
one dependent variable. The independent variable will be plotted
on the x-axis (horizontal). The dependent variable will be plotted
on the y-axis (vertical). This allows us to easily see the result that
the change in the independent variable will have on the dependent
variable.
For example, this graph allows us to see the impact the number
of minutes of heating (independent variable) has on the
temperature of the water (dependent variable).
Scatter Plot
With a scatter plot each mark, represents a single data point. With one mark (point) for every data point a
visual distribution of the data can be seen. Depending on how tightly the points cluster together, you may be
able to discern a clear trend in the data.
Line Graph
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Line graphs are like scatter plots in that they record individual data values as marks on the graph. The
difference is that a line is created connecting each data point together. In this way, the local change
from point to point can be seen. This is done when it is important to be able to see the local change
between any to pairs of points. An overall trend can still be seen, but this trend is joined by the local
trend between individual or small groups of points. Unlike scatter plots, the independent variable can
be either scalar or ordinal. In the example above, Month could be thought of as either scalar or
ordinal. The slope of the line segments are of interest, but we would probably not be generating
mathematical formulas for individual segments.
The above example could have also been produced as a bar graph. You would use a line graph when
you want to be able to more clearly see the rate of change (slope) between individual data points. If
the independent variable was nominal, you would almost certainly use a bar graph instead of a line
graph.
Scatter Plot -
Trend line -
Sample Scatter Plots:
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Positive Correlation
Negative Correlation
No Correlation
Scatterplot Examples:
1.
2.
The correlation seen in the graph below would be best described as:
You are asked to write an equation for the line
of best fit for the scatter plot shown at the right
without the use of a graphing calculator. What
should you do first?
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Choose:
Connect the points together.
Find the slope using (1,2) and (9,12).
Find the slope using (4,6) and (5,8).
Decide which two points give the most
representative straight line.
3. The scatter plot at the right shows the
number of chapters in a book in relation to the
number of typos found in the book. Predict
the number of typos that would occur in a
book with 12 chapters.
4. When making a scatter plot, you should
never:
label the axes
connect the dots
plot more than one y value for any x value
use a graphing calculator
5.
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
HW: p.337 #1-8, 23, 25; practice page (next in notes)
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Additional Graphing Practice:
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Practice Keystone Questions:
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Lesson 7: Permutations and Combinations (PH text 12.6) - optional
Objective: to find permutations and combinations
Multiplication Counting Principle:
If there are m ways to make a first selection and n ways to make a second selection,
then there are m  n ways to make the two selections.
Examples:
1)
You are choosing how to spend Saturday afternoon. You have the option of going rock climbing or
ice skating, with Friend A, Friend B, or Friend C. How many ways are there to decide, if you may
only do one activity with one friend? Create a tree diagram to model your options.
2)
You are making a sandwich with several options. The choices are listed below. How many ways are
there to make your sandwich (assume only one choice from each)?
Bread: whole wheat, white
Meat: turkey, ham, or roast beef
Cheese: American or provolone
Permutations – an arrangement of objects in a specific order
Example: Write the permutations of the letters A, B, and C.
How many different orders could you have with 4 letters?
How many different orders could you have with 5 letters?
(This gets cumbersome to write out. Let’s look for a shortcut!)
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Total #
Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Permutations:
How many different orders could you have with 5 letters?
5∙4∙3∙2∙1 = 5!
n factorial = n! =
Permutation notation - nPr = n objects arranged r at a time
nPr
Example:
1)
2)
Practice using the graphing calculator:
37
=
n!
(n  r )!
Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Combinations – a selection of objects without regard to order
Example: Selecting two side dishes from a list of five, the order does not matter.
A, B, C, D, E
Total #
Combination notation - nCr = the number of combinations of n objects chosen r at a time
n!
n Cr =
r !(n  r )!
Example:
Practice:
1) In how many different ways can you choose four fruits for a fruit salad from 9 different fruits?
Practice using the graphing calculator.
HW: p.754 #11-14, set up the following problems for the calculator: 25-26, 37-39
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Lesson 8: Theoretical and Experimental Probability (PH text 12.7)
Objective:
to find theoretical and experimental probabilities
Key Terms:
outcome – the result of a single trial
sample space – the set of all possible outcomes
event – any of the possible outcomes or group of outcomes
Probability – the likelihood that a particular event will occur – expressed as a ratio
Theoretical Probability – the probability can be predicted when all possible outcomes are equally likely
Theoretical Probability
Example 1:
P(event) = # of favorable outcomes
# of possible outcomes
Flip a coin.
P(heads) =
P(tails) =
Example 2: Roll a six sided number cube.
P(3) =
P(even) =
P(>2) =
You can write the probability of an event as a fraction, decimal, or percent.
All probabilities range from _______ to ________.
A probability of “0” means an event is _______________________ to occur.
A probability of “0.5” means an event is _______________________ to occur.
A probability of “1” means an event is _______________________ to occur.
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Algebra 1
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Unit 3 Notes: Data Analysis and Probability
Complementary events – a set of two opposite situations, that an event does occur and that the event does
not occur -- The complement of an event is the chance that the event will NOT occur.
Complement of an event = 1 – P(event)
Example 3: Spin a numbered spinner.
P(< 3) =
P(not < 3) =
P(6) =
P(not 6) =
Odds –
a ratio that compares the probability of an event to its complement
Odds in favor of an event
P(event) = # of favorable outcomes .
# of unfavorable outcomes
Odds against an event
P(event) = # of unfavorable outcomes
# of favorable outcomes
Example 4: Roll a six sided number cube.
What are the odds of rolling a 4?
P(4) =
1
, then P(not 4) =
6
Odds in favor of the event =
Odds against the event =
What are the odds of rolling a number > 4?
odds against # > 4?
Experimental Probability – the probability is based on data collected from repeated trials
Experimental Probability
P(event) =
# of times the event occurs
.
# of times the experiment is done
HW: p.760 #7-8, 10-36 even
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Algebra 1
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Unit 3 Notes: Data Analysis and Probability
Lesson 9: Probability of Compound Events (PH text 12.8)
Objective: to find probabilities of mutually exclusive and overlapping events
Compound Events – when two or more events are linked by the word “and” or the word “or” – written as an
expression of probabilities of simpler events
Mutually Exclusive Events – when two events have no outcomes in common
A and B are mutually exclusive events if P(A and B) = 0
If A and B are mutually exclusive events, P(A or B) = P(A) + P(B)
Overlapping Events – when two events have at least one outcome in common
If A and B are overlapping events, P(A or B) = P(A) + P(B) – P(A and B)
Examples:
You roll a 20-sided, numbered die.
Mutually Exclusive Events
P(2) =
Overlapping Events
P(multiple of 2) =
P(5) =
P(multiple of 5) =
P(2 or 5) = P(2) + P(5)
P(mult. of 2 or mult. of 5) = P(mult. of 2) + P(mult. of 5) – P(mult. of 2 & 5)
Examples:
You have a bag of colored beads. The beads in the bag are red, orange, yellow, green, blue or
purple. There are an equal number of each color, with a total of 360 beads in the bag.
Mutually Exclusive Events
P(red) =
Overlapping Events
P(primary color) =
P(blue) =
P(red) =
P(red or blue) = P(red) + P(blue)
P(primary or red) = P(primary) + P(red) – P(primary & red)
HW: p.768 #7-16
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Lesson 9b: Probability of Compound Events (PH text 12.8)
Objective: to find probabilities of independent and dependent events
Independent Events – when the outcome of one event does not affect the outcome of a second event (also “with replacement”)
examples – flip a coin, roll a die, pick a card then put it back in the deck
Compound Events - Probability of Two Independent Events –
If A and B are independent events, then P(A and B) = P(A)  P(B)
sample space – the set of all possible outcomes
– a tree diagram can be used to show the possible relationships
Example 1:
You have 2 pennies, 3 nickels and 5 dimes. What is the probability of picking a penny,
replacing it, and then picking a dime?
Example 2: What is the probability of flipping a coin to heads three times in four flips?
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Algebra 1
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Unit 3 Notes: Data Analysis and Probability
Dependent Events - (without replacement) – when the outcome of one event affects the outcome of a
second event
Probability of Two Dependent Events =
If A and B are dependent events, then P(A then B) = P(A)  P(B after A)
Example 3:
You have 2 pennies, 3 nickels and 5 dimes, what is the probability of picking a penny and
then a dime without replacing the penny first?
Example 4:
Suppose you have a dark closet containing seven blue shirts, five yellow shirts and eight
white shirts. You pick two shirts from the closet. Find each probability.
P(blue and yellow shirts) with replacing
P(two yellow shirts) with replacing
P(yellow and white shirts) without replacing
P(two blue shirts) without replacing
Example 5:
Work backwards (write an equation) to solve - Kevin owns only black and white socks.
1
The probability that he picks a whole pair of white socks is . The probability that he picks
3
3
just one white sock is
. What is the probability that he will choose a second white sock?
5
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Algebra 1
Mrs. Bondi
Unit 3 Notes: Data Analysis and Probability
Work backwards (write an equation) to solve –
6)
Penny owns only blue and yellow shirts. The probability that she wears a blue shirt two days in a
3
4
row is
. The probability that she picks a yellow shirt is . What is the probability that she will wear
7
13
blue the next day? (Read carefully!)
7)
A jar contains red and green M & Ms. You pick two (eating the first one). The probability of
158
2
picking two reds is
. The probability of picking one red is . Find the probability of picking a
357
3
second red. How many M & Ms are in the jar?
8)
A bag contains red, white and blue balloons. You pick two balloons without replacing the first one.
7
The probability of drawing a blue and then a white is
. The probability that your second balloons is white
75
1
if your first balloon is blue is . Find the probability that the first balloon is blue.
3
HW: p.768 #18-46 even, 47 (#48 extra credit)
44