Name: ____________________________
Chapter 5: Probability Review
4. a. How many different ways can the letters of BOOBOO can be arranged?
b. How many different ways can the letters of UHOHOOPSIES be arranged?
5. Here is some given information about events X and Y:
 P(X) = 0.35

P(Y | X) = 0.6

P(Y | not X) =
2
3
a. Find P(X and Y).
b. Find P(not X and Y).
c. Find P(Y).
d. Find P(X | Y).
e. Suppose you must change the given information in a way that makes X and Y mutually exclusive.
You are only allowed to change one number. Which number would you change, and to what
would you change it?
f. Go back to the original set of given information. Now suppose you must change the given
information in a way that makes X and Y independent. You are only allowed to change one
number. Which number would you change, and to what would you change it?
6. Mia has 9 pens in her backpack: 6 blue and 3 red. Here are two slightly different questions about the
pens (the only difference is highlighted in bold).
a. Mia randomly takes a pen from her backpack to take notes in English.
She puts the pen away at the end of class.
Next period in Social Studies, again she randomly takes a pen from her backpack.
What is the probability that Mia used a red pen in English and a blue pen in Social Studies?
b. Mia randomly takes a pen from her backpack to take notes in English.
She forgets to put that pen away, leaving it on her English desk.
Next period in Social Studies, again she randomly takes a pen from her backpack.
What is the probability that Mia used a red pen in English and a blue pen in Social Studies?
7. Suppose there are jars A, B, and C containing white and black balls as
shown. A die is rolled.
If the roll is 1 or 2, a ball is drawn from jar A.
If the roll is 3, 4, or 5, a ball is drawn from jar B.
If the roll is 6, a ball is drawn from jar C.
a.
b.
c.
d.
e.
f.
g.
What is the probability of picking Jar A?
What is the probability of picking a black ball given that Jar A has been picked?
Find the probability of picking Jar A and picking a black ball.
Find the probability of picking Jar B and picking a black ball.
Find the probability of picking Jar C and picking a black ball.
Find the probability of picking a black ball.
Find the probability of picking a white ball.
8. Suppose 1 random student is selected from the 525 eighth-graders summarized by this table.
boy
girl
Clarke
132
143
Diamond
120
130
Let D be the event of choosing a Diamond student. Let G be the event of choosing a girl.
a.
b.
c.
d.
Show that D and G are independent using the method P(G | D) = P(G).
Show that D and G are independent using the method P(D | G) = P(D).
Show that D and G are independent using the method P(D and G) = P(D) · P(G).
Identify two events of this experiment that are not independent.
9. In the alphabet, the letters {a, e, i, o, u} are called vowels.
a. If a 3-letter “word” is formed by randomly choosing 3 letters from the word ocean, what is the
probability that it is composed only of vowels?
b. If a 3-letter “word” is formed by randomly choosing 3 letters from the word mountains, what is
the probability that it is composed only of vowels?
10. If A and B are mutually exclusive events and P(A) = 0.3, and P(B) = 0.2, find the following:
a. P(A and B)
b. P(not A)
c. P(A or B)
11. Use the following set up to answer each question:
12. Use the following set up to answer each question:
A local gym wants to gather data on thhe levels of gym membership among adult men and women in
the community. Their research found that 52% of adults on the cimmunity are women, 48% are men.
19% of women have a gym membership, and 85% of men do not have a gym membership.
1. Draw and complete a two-way table to summarize the data.
13. A survey of 85 students asked them about the subjects they liked to study. 35 students liked
math, 37 liked history, and 26 liked physics. 20 liked math and history, 14 liked math and
physics, and 3 liked history and physics. 2 students liked all three subjects. Draw a Venn
Diagram to represent the information.
a. What is the probability that a student did not like Math?
b. What is the probability that a student liked at least 2 subjects?
c. Give an example of a pair of dependent events. Justify your answer.
d. Give an example of a pair of mutually exclusive events. Justify your answer.
e. Are the events “liking math” and “liking physics” independent? Show a calculation to support your
answer.
More review in the textbook
Chapter 5 Review – page 424 #1, 4
Chapter 5 Practice Test – page 425 # 6, 7
Chapter 5: Probability Review Answers
4. a. (62) = (64)
b. 11!/(2!3!2!) = 1,663,200
5. a. P(X and Y) = P(X)× P(Y X) = 0.21
b.
P(not X and Y) = P(not X)× P(Y not X) = 0.433
c.
P(Y) = P(X and Y) + P(not X and Y) = 0.643
P(X and Y)
= .326
P(Y)
d.
e. Need P(X and Y) = 0 so set P(Y X) = 0
f. Need P(Y X) = P(Y) and
P(Y not X) = P(Y) so set
P(Y X) = P(Y not X)
P(X Y) =
6.
a.
æ 3ö æ 6 ö 2
ç ÷× ç ÷ =
è 9ø è 9ø 9
7.
b.
æ 3ö æ 6 ö 1
ç ÷× ç ÷ =
è 9ø è 8ø 4
2 1
æ 1ö æ 3ö 1
=
e. ç ÷× ç ÷ =
6 3
è 6ø è 4 ø 8
1
æ
1 ö æ 1 ö æ 1 ö 35
b.
f. ç ÷ + ç ÷ + ç ÷ =
3
è 9 ø è 4 ø è 8 ø 72
æ 1ö æ 1ö 1
35 37
c. ç ÷× ç ÷ =
=
g. 1 è 3ø è 3ø 9
72 72
æ 3ö æ 2 ö 1
d. ç ÷× ç ÷ =
è 6ø è 4 ø 4
8. a. P(G | D) = 130
, P(G) = 273
b. P( D | G) = 130
, P(D) = 250
250
525
273
525
273
130
c. P(D) = 250
,
P(G)
=
,
P(D
and
G)
=
525
525
525
d. ex. not independent: A = a student from Diamond, B = a student from Clarke.
3!
𝟒∙𝟑∙𝟐
9. a.
b. ((𝟗∙𝟖∙𝟕)⁄(𝟐∙𝟏))
5 P3
10. a. 0
b. 0.7
c. 0.5
a.
11.
12.
13.
a.
b.
c.
d.
50/85
33/85
answers will vary – example: history and physics are dependent because P(P) P(PH)
answers will vary – example: math and not liking any subjects. If you don’t like of the three, how
can you possibly like math?
e. Not independent. Various calculations can confirm this (be able to show all different ways)