Theoretical vs. Practical prob Name: _________________________________
Name: _______________
Date: _____________
Do Now
In at least three sentences, describe what is going on in the situation below.
_________________________
_________________________
_________________________
_________________________
_________________________
_________________________
__________________________________________________
__________________________________________________
The results of a survey of 80 households in Westville are shown below.
1. If Westville has 15,200 households, predict the number of
households that will have exactly 3 computers?
2. How many households will have 2 or 3 computers?
Number of
Computers
Frequency
0
12
1
29
2
31
3
6
More than 3
2
Bourque/Laughton
Probability– Day 1
EXPERIMENTAL VS. THEORETICAL PROBABILITY ACTIVITY
__________________________________ is a value from 0 to 1 that measures the likelihood of an
event.
P(event) =
number of favorable outcomes
number of possible outcomes
In this activity, you will investigate the difference between theoretical and experimental
probability by tossing a coin.
Coin Toss
1. When tossing a coin one time, there are only _____ possible outcomes. What are they?
_____________________________________________________
b. P(tails) =_________
Theoretical Probability
If you toss a coin 10 times, how many heads should you get? __________
Percent=
How many tails should you get? ___________
Toss
1
Percent=
2
Experimental Probability
3
4
Toss your coin 10 times. Record the number of heads. _________
Percent=
5
6
Toss your coin 10 times. Record the number of tails. _________
7
Percent=
8
9
2. Did you get the number of heads and the number of tails
that you expected when you tossed the coins?_____________________
10
Result
EXPERIMENTAL VS. THEORETICAL
_________________________________ probability of an event measures the likelihood that the event
occurs based on actual results of an experiment.
P(event) =
Example 1: A quality control inspector samples 500 LCD monitors and finds defects in
three of them.
a. What is the experimental probability that a monitor selected at random with have
a defect?
b. If the company manufactures 15, 240 monitors in a month, how many are likely
to have a defect based on the quality inspector’s results?
Practice 1: A park has 538 trees. You choose 40 at random and determine that 25 are maple
trees.
a. What is the experimental probability that a tree chosen at random is a maple
tree?
b. About how many trees in the park are likely to be maple trees?
_________________________________ probability describes the likelihood of an event based on
mathematical reasoning.
1
Example 2: You are rolling two dice
numbered 1 to 6. What is the probability
that you roll numbers that add to 7?
1
2
3
Practice 2: What is the probability that
you roll a sum of 9?
4
5
6
2
3
4
5
6
PRACTICE
1. A baseball player got a hit 19 times of his last 64 times at bat.
a. What is the experimental probability that the player got a hit?
b. If the player comes up to bat 200 times in a season, about how many hits is he
likely to get?
2. A medical study tests a new cough medicine on 4,250 people. It is effective for 3982
people.
a. What is the experimental probability that the medicine is effective?
b. For a group of 9000 people, predict the approximate number of people for whom
the medicine will be effective?
3. A bag contains letter tiles that spell the name of the state MISSISSIPPI. Find the
theoretical probability of drawing one tile at random for each of the following.
a. P(M) =
b. P(I) =
c. P(S) =
d. P(P) =
e. P(not M) =
f. P(not I) =
g. P(not S) =
h. P(not P) =
PROBABILITY DISTRIBUTIONS AND FREQUENCY TABLES
A _________________________________ _______________ is a data display that shows how often an item
appears in a category.
The table at the below shows the speeds of cars as they pass a certain mile marker on
highway 66. The speed limit is 65 mph.
a. What is the total number of
cars that pass the marker?
b. What is the probability that a car
stopped at random will be traveling
faster than the speed limit?
Speed
(mph)
Number
of Cars
< 55
2
55 - 60
12
60 - 65
23
> 65
13
_______________________________ _________________________ is the ratio of the frequency of the
category of the total frequency.
Frequency
Example 3: The results of a survey of students’ music
Type of
Music
Preferred
preferences are organized in the frequency table to the
Rock
10
Hip Hop
7
Country
8
Classical
5
Alternative
6
Other
4
right. What is the relative frequency of preference for
rock music?
Practice 3: What is the relative frequency of the
following?
a. Classical
b. Hip Hop
c. Country
PRACTICE
1. A student conducts a probability experiment by tossing 3 coins one after the other. Using
the results below, what is the probability that exactly three heads will occur in the next
three tosses?
Coin Toss
Results
HHH
HHT
HTT
HTH
THH
THT
TTT
TTH
Frequency
5
7
9
6
2
9
10
2
2. A student conducts a probability experiment by spinning a spinner divided into parts
numbered 1 - 4. Using the results in the frequency table, what is the probability of the
spinner pointing at 4 on the next spin?
Spinner
Result
1
2
3
4
Frequency
29
32
21
18
3. In a recent competition, 50 archers shot 6 arrows each at a target. Three archers hit no
bull’s eyes; 7 hit two bull’s eyes; 7 hit three bull’s eyes; 11 hit four bull’s eyes; 10 hit five
bull’s eyes; and 7 hit six bull’s eyes. Fill in the table below.
Number of
Bull’s Eyes
Hit
0
Frequency
3
Probability
3/50
1
2
3
4
5
6
1. The table below shows the number of text messages sent in one month by students at
Metro High School.
Number of
Number
a. If a student is chosen at random, what is the
Texts (t)
of
probability that the student sends 1500 or
Students
fewer text messages in one month?
t < 500
25
b. If a student is chosen at random, what is the
probability that the student sends more than
1500 messages a month?
500 < t < 1500
120
1500 < t < 2500
300
t > 2500
538
Bourque/Laughton
Homework 8-1
Name: _________________________________
Date: _______________
Period: _____________
Homework 8-1: Probability
1. Suppose you flip a coin three times, what is the theoretical probability that you flip
2. A music collection includes 10 rock CDs, 8 country CDs, 5 classical CDs, and 7 hip hop
CDs.
a. What is the probability that a CD randomly selected from the collection is a
classical CD?
b. What is the probability that a CD randomly selected from the collection is
not a classical CD?
3. You are playing a board game with a standard number cube (numbered 1 – 6). It is
your last turn and if you roll a number greater than 2, you will win the game. What is
the probability that you will not win the game?
4. If there is a 70% chance of snow this weekend, what is the probability that it will not
snow?
5. From 15,000 graphing calculators produced by a manufacturer, an inspector selects a
random sample of 450 calculators and finds 4 defective calculators. Estimate the total
number of defective calculators out of 15,000.
6. A student randomly selected 65 vehicles in the student parking lot and noted the color
of each. She found that 9 were black, 10 were blue, 13 were brown, 7 were green, 12
were red, and 14 were a variety of other colors. What is each experimental
probability?
a. P(red) =
b. P(not blue) =
c. P(not green) =
10. The honor society at a local high school sponsors a blood
drive. High school juniors and seniors who weigh over 110
pounds may donate. The table at the right indicates the
frequency of donor blood type.
Blood
Type
Frequency
O
30
A
25
B
6
AB
2
a. What is the relative frequency of blood type AB?
b. What is the relative frequency of blood type A?
c. Which blood type has the highest relative frequency? What is the relative
frequency for this blood type?
d. The blood drive is extended for a second day, and the frequency doubles for
each blood type. Do the relative frequencies change for each blood type?
Explain.
11. Twenty-three preeschoolers were asked what there
favorite snacks are. The results are show in the bar
graph to the right.
a. What is the probability that a preschooler
chosen at random chose popcorn as their
favorite snack?
a. What is the probability that a preschooler
chosen at random did not chose bananas as
their favorite snack?
a. Complete the table below.
Snack
Popcorn
Frequency
6
Probability
6/23
Celery and
Cheese
Trail Mix
Bananas