Deck 10: Probability

Question 1

At a banquet for 300 people, one TV, three turkeys, and six symphonic records are to be awarded as door prizes. Ten slips of paper, each with the name of a prize on it, have been hidden under 10 of the dinner plates on a random basis. What is the probability that a particular guest will win
(a) the TV
(b)a symphonic record
(c)a door prize of some kind

Answer 1

(a).0033
(b).02
(c).033.

Question 2

A slot machine has three wheels that rotate independently. When the lever is pulled, the wheels rotate and then come to a stop, one by one, in random positions. The circumference of each wheel is divided into 25 equal parts and contains four pictures each of six different fruits and one picture of a jackpot label. What is the probability that the following will appear under the window on the middle wheel:
(a)a jackpot label?
(b)an orange?
(c)a fruit?

Answer 2

(a).04
(b).16
(c).96.

Question 3

Suppose you pull the lever on the slot machine described in Problem 2. What is the probability that
(a) either an orange or a lemon or a jackpot label will appear on the middle wheel?
(b)a jackpot label will appear on all three wheels?
(c)cherries will appear on all three wheels?

Answer 3

(a).36
(b).000064
(c).004.

Question 4

Suppose we make three consecutive random selections from this group of 200 students. After each selection, we record the grade and sex of the individual selected and replace him or her back in the group before making our next selection. First, determine the following three probabilities for a single selection: the probability of a male "B" student, a male "A" student, a female student. Now, apply the appropriate rule(s) to these probabilities to determine the probability that
(a) the first selection is male with a grade of at least B;
(b)the second selection is a male with a grade of B or a female;
(c)the first selection is a male with a grade of B and the second selection is a female;
(d)all three selections are males with a grade of B or better.

Question 5

Two fair dice are rolled. What is the probability of
(a) an even number or a three on the first die?
(b)an even number on the first die and a three on the second?

Question 6

In which of the following instances are the events mutually exclusive?
(a)Obtaining a head on the first toss and a tail on the second toss of a coin.
(b)Being a male and being pregnant.
(c)Being 45 years old and being pregnant.
(d)Obtaining a grade of A and obtaining a grade of C in your first course in statistics.
(e)Obtaining three aces in two consecutive hands dealt each time from a complete, well-shuffled deck of playing cards.
(f)Disliking music and attending a concert.
(g)Obtaining a three and an even number on a single roll of a die.
(h)Winning on one play of a slot machine and winning on the very next play.
(i)Being 15 years old and voting in the last national election.

Question 7

A class is administered a test consisting of five four-alternative multiple-choice items.?
(a)List the ways in which one could obtain a score of four correct on this test.
(b)What is the probability of obtaining a score of exactly four correct by guessing randomly on each item?
(c)What is the probability by guessing randomly of obtaining a perfect score on the test?
(d)What is the probability of obtaining a score of four correct or better on the test by guessing randomly?
(e)What is the probability of missing all five items through random guessing?

Question 8

A slot machine has three wheels that rotate independently. When the lever is pulled, the wheels rotate and then come to a stop, one by one, in random positions. The circumference of each wheel is divided into 25 equal parts and contains four pictures each of six different fruits and one picture of a jackpot label.

-Suppose you pull the lever on the slot machine of above. What is the probability that
(a) an orange will appear on exactly two of the wheels?
(b)an orange will appear on at least two of the wheels?
(c)a jackpot label will appear on at least one of the wheels?

Question 9

The probability of an event may be thought of as the proportion of times that event occurs in

A) an infinite series of trials
B) a large sample of trials
C) any trial
D) a specific trial

Question 10

For a fair coin, fairly tossed, we say that the probability of it coming up heads is .50. This is an example of

A) empirical probability
B) theoretical probability
C) the addition theorem
D) the multiplication theorem

Question 11

The probability of occurrence of any one of several events is the sum of their individual probabilities when

A) the events are independent
B) the events are mutually exclusive
C) sampling is random
D) that sum is not less than zero nor greater than one

Question 12

The probability of joint occurrence of several events is the

A) sum of the probabilities of the several events
B) sum of the probabilities of the several events when the events are independent
C) product of the probabilities of the several events when the events are mutually exclusive
D) product of the probabilities of the several events when the events are independent

Question 13

Two events are independent if

A) one is the complement of the other
B) they are mutually exclusive
C) the outcome of one is unaffected by the occurrence (or not) of the other
D) one must occur if the other does not

Question 14

Which of the following pairs of events illustrate statistical independence?

A) being a woman and being in the military service
B) obtaining a 3 and an even number on a single roll of a six-sided die
C) obtaining a 2 and an even number on a single roll of a die
D) obtaining a 2 and an even number on two consecutive rolls of a die

Question 15

And:or as

A) multiplication:division
B) multiplication:addition
C) addition:division
D) addition:multiplication

Question 16

A pile of jelly beans consists of 6 dark green, 4 light green, 6 blue, and 4 red. If one jelly bean is selected at random, the probability of its being green is

A) .10
B) .2
C) .06
D) .50

Question 17

A card is drawn from a well-shuffled deck of 52 playing cards. The probability of drawing the king of hearts is

A) 1/52
B) 4/52
C) 13/52
D) 1/13

Question 18

A card is drawn from a well-shuffled deck of 52 playing cards. The probability of drawing a king is

A) 1/52
B) 4/52
C) 13/52
D) 1/2

Question 19

A card is drawn from a well-shuffled deck of 52 playing cards. The probability of drawing an ace or a king is

A) 1/52
B) 2/6
C) 4/52
D) 8/52

Question 20

A six-sided die is rolled twice. What is the probability that the first roll will come up 1 and the second 2?

A) 1/6
B) 2/6
C) 1/36
D) 2/36

Question 21

A six-sided die is rolled twice. What is the probability that the first roll will come up 2 and the second 1?

A) 1/6
B) 2/6
C) 1/36
D) 2/36

Question 22

The probabilities of occurrence of events A, B, and C are .2, .3, and .3, respectively. If any one of the events occurs, the others can't. What is the probability of either A or C occurring?

A) .06
B) .80
C) .50
D) can't be determined from what is given

Question 23

The probabilities of occurrence of independent events D, E, and F are .3, .1, and .2, respectively. The probability of all three occurring is

A) .6
B) .06
C) .006
D) can't be determined from what is given

Question 24

The probability of a run of four straight heads on four consecutive flips of a fair coin is

A) .0625
B) .1250
C) .0002
D) .0375

Question 25

The probability of obtaining a perfect score on a 3-item multiple choice test (4 alternatives per item) by random guessing is

A) .7500
B) .0156
C) .0003
D) .1250

Question 26

The probability of obtaining a score of 1 correct on a 4-item true-false test by random guessing is

A) 2/16
B) 3/16
C) 4/16
D) 6/16

Question 27

The probability of obtaining a score of 1 correct on a 2-item multiple choice test (4 alternatives per item) by random guessing is

A) 2/16
B) 3/16
C) 4/16
D) 6/16

Question 28

The number of ways one can obtain 2 heads out of 3 flips of a coin is

A) 3
B) 4
C) 1
D) 2

Question 29

The probability of obtaining 2 heads out of 3 flips of a coin is

A) 1/4
B) 3/8
C) 3/16
D) 1/8