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Review
Ch. 5 – Probability
A/ Page 362 #1-4, 6-9, 12-17, 19-24
B/ Venn Diagrams: Draw a Venn diagram for each situation, then answer the questions.
1. In a school of 320 students, 85 students are in the band, 200 students are on sports teams, and 60
students participate in both activities. How many students are involved in either band or sports?
2. In a survey of 250 students, 166 have part time jobs, 124 are involved in school sports, and 41 take
music lessons. Also, 15 have part time jobs and take music lessons, 84 are in sports and have a job, and
22 are in sports and music lessons. Only 8 students have jobs and are involved in sports and music.
a.
How many are involved in none of these activities?
b.
How many are involved in either sports or music (or both)?
c.
How many have part-time jobs, but aren’t involved in either sports or music?
d.
If a student is randomly selected from this group, what is the probability that the student is
involved in exactly two of these three activities?
C/ From January 2005 Exam:
22. Two dice are tossed. What is the probability that they will land on different numbers?
30
6
5
2
A.
B.
C.
D.
36
36
36
36
23. A bag contains 12 green marbles, 10 red marbles and 18 white marbles. Bill removes 1 marble from
the bag. The probability that Bill removes a red marble from the bag is
1
1
1
1
A.
B.
C.
D.
4
10
3
40
24. If an event can succeed in ‘s’ ways and fail in ‘f’ ways, then the probability of success is
s
s
A.
B.
C. s  f
D. 1 – f
f
f s
25. In a school of 200 students, 80 have blood type O. If 5 students are chosen at random, what is the
probability of selecting five students with type O blood?
C
5
5
1 1
1
1
1
   
A.
B.
C.
D. 80 5
80 79 78 77 76
80 C 5
80 P5
200 C 5
41. One card is selected from a standard deck of 52 playing cards. What is the probability that the card
selected is a diamond or an ace?
42. From a group of 5 men and 6 women, what is the probability that a committee formed at random will
consist of 3 men and 3 women?
43. Joe, Mary, and George are among the seven finalists for a random draw to win three different prizes.
What is the probability that Joe will win 1st prize, Mary will win 2nd prize, and George will win 3rd prize?
Express your answer in fraction form.
44. John, Amy, and Fred tried to solve the following problem:
In a certain city, during a person’s lifetime the probability of having diabetes is 0.10 and the probability of
having cancer is 0.05. What is the probability of a person having either diabetes or cancer in his/her
lifetime?
Suppose that event C is ‘person having cancer’ and event D is ‘person having diabetes’.
Their proposed solutions are as follows:
John’s solution:
P(C and D) = 0.10 x 0.05 = 0.005
Amy’s solution:
P(C or D) = 0.10 + 0.05 = 0.15
Fred’s solution:
P(C or D) = 0.10 + 0.05 – 0.005 = 0.145
(a) Which student has the correct answer?
(b) Explain why the other two solutions are NOT correct.
D/ From June 2005 exam:
22. Consider the following Venn diagram.
Event K
Event L
Which of the following is correct?
A. P(K or L) = P(K) + P(L)
C. P(K or L) = P(K) x P(L)
B. P(K and L) = P(K) + P(L)
D. P(K and L) = P(K) x P(L)
23. Your math teacher gives your class a list of eight questions to study. Five of the eight questions will
be randomly selected for the next test. If you study only the first five questions from the list, the
probability that all of those five questions will be on the test is
1
1
5
1
A.
B.
C.
D.
8
8
8 C5
8 P5
500!
is
499!
B. 1.002
24. The value of
A. 1
C. 500
D. undefined
25. A bag contains 9 marbles, 4 of which are red. What expression represents the probability of selecting
three red marbles when three marbles are drawn at random?
1
4
4
1
A.
B.
C.
D.
9 C3
9 C3
9 P3
9 P3
41. There are 15 jellybeans randomly distributed in a jar; 5 are yellow and 10 are orange. You reach into
the jar and, without looking, remove 2 jellybeans. What is the probability that you will remove 2 yellow
jellybeans?
42. In a group of 15 people, 4 are left-handed and 11 are right-handed. Seven people are selected at
random from this group.
(a) What is the probability that everyone selected is right-handed?
(b) If Sarah and Mike, two of the left handers, have already been chosen, what is the probability that all
the other members selected will be right-handed?
43. Create a real-life problem that demonstrates P(A or B) = P(A) + P(B) – P(A and B) when the events
A and B are NOT mutually exclusive. (You don’t have to solve the problem).