Chapter 4 - Probability
1. The chances of a family having a boy is simulated by tossing a coin ten times. Heads is used to simulate having a girl and tails is used to simulate
having a boy. Out of ten trials, two heads and eight tails turn up. This experimental probability of
is
a) close to the theoretical probability b) equal to the theoretical probability c) not close to the theoretical probability d) none of the above
2. Two dice are rolled. The probability of rolling a sum less than 5 is
a)
b)
c)
d)
3. A spinner is divided into twelve equal sectors, numbered 1 through 12. An event space is defined as spinning a number divisible by 3. The value of
is
a)
b)
c)
d)
4. A student writes a multiple choice test that consists of 3 questions, each with 4 choices. What is the probability of the student have a perfect mark on
the test by guessing?
a)
b)
c)
d) none of the above
5. In a hat, there are 2 nickels and 2 dimes. If two coins are chosen at random at the same time, the probability that both are nickels is
a)
b)
6. Let set
a)
c)
d)
be the set of even numbers between 1 and 20. Let
b)
c)
be the set of all numbers divisible by three between 1 and 20. Which statement is true?
d)
7. The probability that John will be accepted into the business program at Probability College is 0.6. The probability that he will be accepted into the
science program is 0.2. The probability that he will be accepted into both programs is 0.1. What is the probability that he will be accepted into at least
one of the programs?
a) 0.7 b) 0.9 c) 0.12 d) none of the above
8. In a high school of 1000 students, 355 are playing sports and 233 are in a school band. If there are 175 students playing sports and are in a school
band, how many are in neither activity?
a) 237 b) 825 c) 413 d) 587
9. The probability that it will be rainy tomorrow is 0.7. The probability that it will be rainy the day after is 0.4. The probability that it will rain tomorrow
and the next day is 0.2. What is the probability that it will rain neither day?
a) 0.7 b) 0.1 c) 0.3 d) none of the above
10. The intersection of two sets is best associated with the word
a) both b) and c) or d) none of the above
11. Ten people each chose a random number from 1 to 20. What is the probability that at least two of them chose the same number?
a) 7% b) 93%
c) 10%
d) 90%
This table refers to questions 12 and 13.
Gender
Males
Females
Mathematics
4
7
English
9
8
12. A class is surveyed to determine whether they prefer mathematics or English. The table above shows the results. Given that a student is male, state
the probability that mathematics is preferred.
a)
b)
c)
d) none of the above
13. A class is surveyed to determine whether they prefer mathematics or English. The table above shows the results. State P(male|prefers English).
a)
b)
c)
d) none of the above
14. From a survey of 500 drivers, 200 drive cars, 120 drive SUVs, 60 drive minivans, and the rest drive trucks.
Determine P(truck driver|not a car driver).
a)
b)
c)
d) none of the above
15. Determine the probability of drawing a face card and then an ace from a regular deck of cards if the face card is not returned.
a)
b)
c)
d)
16.
State the probability of a family having two girls and one boy, not necessarily in that order.
a)
b)
c)
d)
17. A bag of marbles contains 4 blue marbles, 7 red marbles, and 3 yellow marbles. A marble is drawn and then replaced. A second marble is then
drawn. Determine the probability of drawing two red marbles.
a)
b)
c)
d)
18. A three-digit code using the numbers 1 to 4 is given to a student at his high school. Determine the probability that the last two digits of the number
are both 4.
a)
b)
c)
d)
19. A tennis player's serve goes in 70% of the time. If he makes three serves, determine the probability of getting the second one in.
a) 0.063 b) 0.70 c) 0.21 d) none of the above
20
Determine the number of three letter arrangements using the letters of the word METAPHOR.
a) 336 b) 40 320 c) 512 d) 56
21. Determine the number of ways that a prime minister, secretary, treasurer, and publicity minister could be chosen from an art club of 12 members.
a) 495 b) 48 c) 11 880 d) 20 736
22. Determine the number of ways you could line up 3 orange marbles, 5 blue marbles, and 1 purple marble.
a) 504 b) 362 880 c) 24 192 d) 15
23. Determine the number of ways that the 12 members of the boys' baseball team can be lined up if Joe, Tanner, and Josh must all be together.
a) 21772800
b) 362880
c) 479001600
d) 27
24. Express 15  14  13 in a different manner.
a) P(15, 13) b)
c)
d) P(15, 12)
25. The letters of the word CHEMISTRY are put in a hat and three letters are drawn, one at a time, without replacement. Determine the probability that
the C and R are chosen.
26. The expression
a)
is equivalent to
a) 42
b)
c)
d)
b)
c) 21
d) 3.5
27. From a group of seven junior and ten senior students, determine how many committees of six students can be chosen if four are junior students.
a) 32 400 b) 675 c) 1350 d) 1575
28. From a group of seven junior and ten senior students, determine how many committees of six students can be chosen if at least one student is a senior
student.
a) 24 738 b) 2944 c) 12 369 d) 1472
29. The starting line up of a co-ed volleyball team must be made up of 3 males and 3 females. If the team has 9 females and 8 males, determine the
probability that Emma, Mary, and Brittany are selected for the line up.
a)
b)
c)
d)
30. A bag contains six blue marbles, seven red marbles, and four green marbles. If four marbles are drawn randomly, determine the probability that three
are green.
a)
b)
c)
d)
Chapter 4 ANSWERS:
1
C
2
A
3
D
4
B
5
C
6
A
7
A
8
D
9
B
10
B
11
B
12
B
13
A
14
B
15
A
16
B
17
C
18
D
19
B
20
A
21
C
22
A
23
A
24
C
25
D
26
C
27
D
28
C
29
B
30
C