7th GRADE UNIT 9: Probability
LESSON 1: Probability
LESSON 2: Experimental Probability
LESSON 3: Sample Space
LESSON 4: Compound Events
LESSON 5: Simulate Compound Events
LESSON 6: Review
LESSON 7: Test
LESSON 1: Probability
OBJECTIVE: To find the probability and the complement of an event.
An ____________ is the result of an action.
Example:
An ___________ is a collection of possible outcomes.
If all the outcomes are equally likely, you can use a formula to find theoretical probability.
THEORETICAL PROBABILITY:
Theoretical Probability =
You can express probability as a ___________, __________ or a _________.
Example 1: Find the probability of selecting a vowel from the letters F, G, H, I. Express the probability
as a fraction, decimal, and a percent.
Example 2: Find P(vowel) from the alphabet. Express your answer as a fraction.
Example 3: Find P(consonant) from the alphabet. Express your answer as a decimal and a percent.
Example 4: Use the definition of probability to find the probability of the spinner landing on each
color.
Example 5: Consider a jar that contains marbles. Suppose that each marble has an equal chance of
being picked from the jar. Find P(blue), P(red), and P(green).
All probabilities __________ from 0 to 1.
A probability of 0 means the event is ______________.
A probability of 1 means the event is _________ to happen.
The ________________ of an event is the collection of outcomes not contained in the event. The
________ of the probabilities of an event and its complement is ___.
Example 6: Charlene has 12 plastic cups. Of the 12 plastic cups, 3 are green, 4 are red, and 5 are
blue. She stacks the cups into a single stack in random order. What is the probability that the cup on
top of the stack is not green?
Example 7:
Examples 8a – 8c: Chad has 1 blue shirt, 5 white shirts, 3 green shirts, and 2 brown shirts. He
selects a shirt a random (shuts his eyes) from his closet. Find each probability.
a.) P(white shirt)
b.) P(not green shirt)
c.) P(blue shirt)
Examples 9a – 9e: You roll a number cube (dice) once. Find each probability.
Possibilities:
a.) P(multiple of 3)
b.) P(not a multiple of 2)
c.) P(3)
d.) P(7)
d.) P(number less than 4)
e.) P(number less than 9)
When outcomes are equally likely, you can write ratios, called ODDS, that compare ______________
outcomes to _________________ outcomes.
ODDS IN FAVORABLE =
ODDS IN AGANIST =
Examples 10a – 10c: You roll a number cube.
Find the odds in favor of each outcome.
a.) rolling a 3
b.) rolling a multiple of 2
c.) rolling an even number
Examples 11a – 11c: Find the odds in against of each outcome.
a.) rolling a 5
b.) rolling a multiple of 3
c.) rolling an odd number
Example 12: The table on the right shows the numbers of game chips of different colors in a bag.
Danielle randomly selects one chip from the bag. Which statement about the selection is true?
A. The probability of selecting a red chip is 1/3.
B. Selecting a yellow, green, or blue chip is certain.
C. The probability of selecting a green chip is 1/20.
D. Selecting a blue or red chip is less likely than selecting a yellow chip.
LESSON 2: Experimental Probability
OBJECTIVE: To find experimental probability and to use simulations.
BELL RINGER: In a stack are several number cards: three 1s, four 2s, three 3s, two 4s, two 6s, and
six 7s. You pick a card at random. Write you answer as a fraction, decimal, and a percent.
a.) P(3)
b.) P(not 7)
NOTES
Probability based on experimental ______ or ________________ is called EXPERIMENTAL
PROBABILITY.
EXPERIMENTAL PROBABILITY:
P(event) =
Example 1: In 60 coin tosses, 25 are tails. Find the experimental probability.
Example 2: A player makes 7 free throws out of 12 attempts. Based on this, what is the
experimental probability of this player making a free throw?
Example 3: A bicycle company checks random sample of bikes. The results are shown. If the trend
continues, which is the best prediction of the number of defective bikes in a batch of 1,300?
QUALITY CONTROL RESULTS
DEFECTIVE BIKES
BIKES CHECKED
12
400
a.) 430 bikes
b.) 390 bikes
c.) 43 bikes
d.) 39 bikes
Examples 4a – 4b: A manufacturer of computer parts checks 100 parts each day. On Monday, 2 of
the checked parts are defective.
a.) What is the experimental probability that a part is defective?
b.) Predict the probable number of defective parts in Monday’s total prediction of 1,250 parts.
You can __________, or model, events to find experimental probabilities.
Example 5: Find the experimental probability that 2 of the 3 children in a family are girls. Assume
that girls and boys are equally likely.
TTH
TTH
HHT
THT
TTT
HHT
TTH
THT
HTH
HTT
THH
THT
HTT
THT
HTH
HHH
HTH
HHH
THT
HHH
Example 6: Use the simulation above to determine the experimental probability that 3 children are all
boys.
LESSON 3: Sample Space
OBJECTIVE: To make and use simple sample spaces and to use the counting principle.
BELL RINGER: A manufacturer makes computer circuit boards. A random check of 5,000 circuit
boards shows that 25 are defective. Predict the number of defective circuit boards per month if the
company manufactures 41,000 circuit boards in July.
NOTES
The collection of all possible outcomes in an experiment is the __________ _________.
You can use sample spaces to find the ______________ of an event.
Example 1: Create a sample space for tossing two coins. What is the probability of getting two
heads?
Example 2: Make a table to find the sample space for rolling two number cubes. Write the outcomes
as ordered pairs.
Examples 3a – 3f: Use your sample spaces for rolling two number cubes to answer the following
questions.
a.) P(rolling at least one 3)
b.) P(sum of 7)
c.) P(sum of 11)
d.) P(sum of 12)
e.) P(sum less than 4)
f.) P(sum greater than 10)
You can also show a sample space by using a ________ _____________. Each branch of the tree
represents ________ choice.
Example 4: Suppose you own an ice cream parlor. You offer 4 types of toppings (chocolate syrup, oreo
cookie crumbles, rainbow jimmies, and cherries) and 3 types of ice cream (vanilla, chocolate, and
strawberry). Each ice cream comes with one topping. How many choices do your customers have when
ordering their ice cream dish?
Example 5: Suppose you can go west or northwest by train, bus, or car.
a.) Draw a tree diagram to show the sample space.
b.) What is the probability of a random selection that results in a bus trip west?
Examples 6a – 6c: Suppose you are going to travel on a river. You have three choices of boats – a
kayak, a rowboat, or a canoe. You can go upstream on three smaller streams, to north, northwest,
and northeast.
a.) Make a tree diagram for the possible outcomes.
b.) Find the probability of selecting a canoe at random for your trip.
c.) What is the probability of selecting a kayak and going directly north?
THE COUNTING PRINCIPLE:
Suppose there are m ways of making one choice and n ways of making a second choice. Then there
are __________________ to make the first choice followed by the second choice.
Example 7: If you can choose a shirt in 5 sizes and 7 colors, then you can choose among?
Example 8: How many kinds of coin purses are available if the purses come in small or large sizes
and colors red, blue, yellow, and black?
Example 9: When you get ready to get dressed for school you open your closet to find that you have
the following choices: a red, blue, or white shirt; jeans or sweatpants; tennis shoes or sandals. How
many different outfits could be made with these choices?
LESSON 4: Compound Events
OBJECTIVE: To find the probability of independent and dependent events.
BELL RINGER: You pick a card at random from cards labeled 1, 2, or 3 and then spin a spinner
divided into thirds, each of which is labeled with number 1, 2, or 3. What is the probability of picking a
card and spinning the same number?
NOTES
A ____________ __________ consists of two or more events.
Two events are ______________ _________ if the occurrence of one event ____________ affect the
probability of the occurrence of the other.
Example:
PROBABILITY OF INDEPENDENT EVENTS:
If A and B are independent events, then P(A, then B) =
Example 1: You and a friend play a game twice. Assume P(win) is ½. What is the probability that
you win both games? Find P(win, then lose).
Example 2: A box contains the same number of green marbles, orange marbles, and blue marbles.
You draw one marble, replace it, and draw a second marble. What is the probability that both
marbles you draw are blue?
Example 3:
Two events are _______________ __________ if the occurrence of one event _________ the
probability of the occurrence of the other event.
Example:
PROBABILITY OF DEPENDENT EVENTS:
If event B depends on event A then, P(A, then B) =
Example 4: You select a card at random from the letter cards that spell MATHEMATICS. The card
has the letter M. Without replacing the M card, you select a second card. Find the probability that
you select a card with the letter A after you select M.
Example 5: You select a card at random from those having A, E, I, O, U, P, C. The card has the
letter E. Without replacing the E card, you select a second card. Find the probability of selecting a
card that does not have a vowel.
Example 6: A bag containing 3 red marbles, 4 white marbles, and 1 blue marble. You draw one
marble. Without replacing it, you draw a second marble. What is the probability that the two marbles
you draw are red, then white?
Example 7: You select a card from a bucket that contains 26 cards letter A-Z without looking.
Without replacing the first card, you select a second one. Find the probability of choosing C and then
M.
Example 8:
LESSON 5: Simulating Compound Events
OBJECTIVE: To design and use simulations to estimate the probability of compound events.
BELL RINGER: You draw a card at random from a stack of ten cards, each labeled with a number
from 1 through 10. Then you draw a second card without replacing the first card.
What is P(5, then 3)?
NOTES
A SIMULATION is a model used to estimate the probability of an event.
Each TRIAL of a simulation results in an outcome.
Example 1: A cereal company marks 1/6 of its box lids with stars. If a customer gets a star, he or
she wins a prize. Design a simulation for estimating the probability that a customer will need to buy at
least 3 boxes to win a prize.
STEP 1: Choose a simulation tool.
STEP 2: Decide which outcomes are favorable.
STEP 3: Describe a trial.
Example 2: One-fourth of the deer population has a certain disease. Design a simulation for
estimating the probability that a scientist will need to test no more than 3 deer before finding one with
the disease.
STEP 1: Choose a simulation tool.
STEP 2: Decide which outcomes are favorable.
STEP 3: Describe a trial.
Example 3: One-third of the voters in a district want a new city park. Design a simulation that can be
used to estimate the probability that a reprehensive will need to interview no more than 3 voters
before finding one who wants the new city park.
STEP 1: Choose a simulation tool.
STEP 2: Decide which outcomes are favorable.
STEP 3: Describe a trial.
Example 4: Perform 20 trials of the simulation you design in the cereal box example. Then estimate
the probability that a customer will need to buy at least 3 cereal boxes to win a prize.
Example 5: Perform 20 trials of the simulation you design in the deer example. Then estimate the
probability that a scientist will need to test no more than 3 deer before finding one that has the
disease.
Example 6: In an election, 52% of voters chose Mayor Garner. Use random digits as a simulation
tool to estimate the probability that a reporter will ask more than 2 voters before finding one who
voted for Garner.
Random Numbers
06 82
80 17
87 65
96 96
60 68
47 39
40 31
66 17
30 33
20 68
Example 7: In the U.S., 42% of blood donors have type A blood. Use the random numbers below as
a tool to estimate the probability that it will take at least 4 donors to find one with type A blood.
91
72
54
70
67
33
58
49
78
21
Medicine
04 81
45 45
93 14
28 66
37 29
77 57
84 14
45 20
05 88
83 16
49
96
81
00
45
22
80
59
88
98