Deck 11: Probability

Question 1

Event 3C
Given the following event:
Given an urn containing 3 white, 4 blue, and 5 pink balls. Two balls are drawn and the first ball is not replaced before the second is drawn.
Given Event 3C, what is the probability that both balls are blue?

A) 7/132
B) 1/12
C) 1/9
D) 2/25
E) 1/11

Answer 1

1/11

Question 2

What is the probability of getting at least 1 head on 4 successive tosses of a coin?

A) 31/32
B) 7/8
C) 3/4
D) 13/16
E) 15/16

Answer 2

15/16

Question 3

To compute the probability of drawing two aces from a poker deck (without replacing the first card before drawing the second) the theory of probability that would normally be used is the:

A) Conditional theory.
B) Subjectivist theory.
C) Classical (a priori) theory.
D) Relative frequency theory.
E) Relativist theory.

Answer 3

Classical (a priori) theory.

Question 4

Event 1B
Given the following event:
Suppose an irregular 7-sided solid object, having sides numbered 1 through 7, is rolled 100 times, and side 4 turns up 12 times.
What is the approximate probability of Event 1B happening?

A) .33
B) .12
C) 1/12
D) 1/7
E) 7/12

Question 5

On one roll of a pair of dice, what is the probability of the points adding up to 4?

A) 1/12
B) 1/6
C) 1/11
D) 1/9
E) 1/8

Question 6

Event 1B
Given the following event:
Suppose an irregular 7-sided solid object, having sides numbered 1 through 7, is rolled 100 times, and side 4 turns up 12 times.
In regard to Event 1B, what are the odds?

A) 1 to 4.
B) 7 to 100.
C) 7 to 125.
D) 3 to 25.
E) 3 to 22.

Question 7

To compute the probability of the Chargers football team beating the Patriots, the theory of probability that would normally be used is the:

A) Relativist theory.
B) Conditional theory.
C) Classical (a priori) theory.
D) Subjectivist theory.
E) Relative frequency theory.

Question 8

To compute the probability of having a fair coin turn up heads four times on four tosses, the theory of probability that would normally be used is the:

A) Conditional theory.
B) Classical (a priori) theory.
C) Subjectivist theory.
D) Relative frequency theory.
E) Relativist theory.

Question 9

To compute the probability of having a loaded die turn up six, the theory of probability that would normally be used is the:

A) Relative frequency theory.
B) Classical (a priori) theory.
C) Subjectivist theory.
D) Conditional theory.
E) Relativist theory.

Question 10

Event 2C
Given the following event:
Given two urns, one containing 3 white, 4 blue, and 5 pink balls, and the other containing 2 white, 3 blue, and 7 pink balls. A single ball is drawn from each.
Given Event 2C, what is the probability that at least one ball is blue?

A) 5/12
B) 7/12
C) 1/2
D) 11/24
E) 3/8

Question 11

Event 1C
Given the following event:
Suppose an irregular 5-sided solid object, having sides numbered 1 through 5, is rolled 100 times, and side 3 turns up 16 times.
What is the approximate probability of Event 1C happening?

A) .08
B) .32
C) 1/16
D) .20
E) .16

Question 12

Event 2C
Given the following event:
Given two urns, one containing 3 white, 4 blue, and 5 pink balls, and the other containing 2 white, 3 blue, and 7 pink balls. A single ball is drawn from each.
Given Event 2C, what is the probability that both balls are pink?

A) 17/72
B) 35/144
C) 19/72
D) 1/4
E) 2/7

Question 13

Event 3C
Given the following event:
Given an urn containing 3 white, 4 blue, and 5 pink balls. Two balls are drawn and the first ball is not replaced before the second is drawn.
Given Event 3C, what is the probability that at least one ball is either white or blue?

A) 9/11
B) 119/144
C) 10/72
D) 28/33
E) 29/33

Question 14

Event 1C
Given the following event:
Suppose an irregular 5-sided solid object, having sides numbered 1 through 5, is rolled 100 times, and side 3 turns up 16 times.
In regard to Event 1C, what are the odds?

A) 5 to 21.
B) 5 to 16.
C) 4 to 25.
D) 4 to 21.
E) 3 to 16.

Question 15

What is the probability of drawing two hearts from a poker deck (no jokers) if the first card is not replaced before the second is drawn?

A) 13/51
B) 1/16
C) 13/52
D) 1/17
E) 1/32

Question 16

To compute the probability of one team winning against another in a sporting event, the theory of probability that would normally be used is the:

A) Classical (a priori) theory.
B) Conditional theory.
C) Subjectivist theory.
D) Relativist theory.
E) Relative frequency theory.

Question 17

Given an urn containing 3 red balls, 4 green balls, and 5 yellow balls. What is the probability of drawing either a red ball or a green ball on a single draw?

A) 7/12
B) 1/2
C) 2/5
D) 2/3
E) 3/7

Question 18

If the odds of the Steelers beating the Chiefs are 7 to 4, what is the probability of this event happening?

A) 4/7
B) 1/11
C) 7/11
D) 4/11
E) 7/4

Question 19

What is the probability of drawing a red king from a poker deck (no jokers) on a single draw?

A) 1/4
B) 1/26
C) 1/52
D) 1/13
E) 2/13

Question 20

According to the principle of indifference,

A) All possible outcomes of an event are equally probable.
B) It makes no difference who conducts the experiment.
C) Some possible outcomes are so unlikely that they are ignored.
D) All possible outcomes are invariant as to time and place.
E) The probability of an event is the same regardless of what theory is used to calculate it.

Question 21

To compute the probability that a mass produced rocket engine would fail prematurely, the theory of probability that would likely be used is the:

A) Classical (a priori) theory.
B) Relative frequency theory.
C) Subjectivist theory.
D) Conditional theory.
E) Relativist theory.

Question 22

What is the probability of drawing a black jack from a poker deck (no jokers) on a single draw?

A) 2/13
B) 1/4
C) 1/26
D) 1/13
E) 1/52

Question 23

Event 1A
Given the following event:
Suppose an irregular 4-sided solid object, having sides numbered 1 through 4, is rolled 100 times, and side 3 turns up 28 times.
What is the approximate probability of Event 1A happening?

A) 3/28
B) 7/25
C) 7/32
D) 1/7
E) 3/7

Question 24

Event 1A
Given the following event:
Suppose an irregular 4-sided solid object, having sides numbered 1 through 4, is rolled 100 times, and side 3 turns up 28 times.
In regard to Event 1A , what are the odds?

A) 7 to 18
B) 7 to 32
C) 7 to 25
D) 3 to 28
E) 1 to 7

Question 25

Given an urn containing 2 pink balls, 3 green balls, and 5 yellow balls. What is the probability of drawing either a green ball or a yellow ball on a single draw?

A) 2/25
B) 3/20
C) 3/4
D) 9/10
E) 4/5

Question 26

To compute the probability of the LA Lakers defeating the Boston Celtics in their upcoming game, the theory of probability that would typically be used is the:

A) Relative frequency theory.
B) Conditional theory.
C) Classical (a priori) theory.
D) Relativist theory.
E) Subjectivist theory.

Question 27

Event 2B
Given the following event:
Given an urn containing 2 green, 3 white, and 4 red balls. Two balls are drawn and the first ball is not replaced before the second is drawn.
Given Event 2B, what is the probability that the first ball is white and the second is red?

A) 2/3
B) 7/17
C) 4/27
D) 1/6
E) 2/9

Question 28

What is the probability of getting at least 1 head on 3 successive tosses of a coin?

A) 1/8
B) 3/4
C) 5/8
D) 15/16
E) 7/8

Question 29

If the odds of the Dodgers defeating the Astros are 4 to 5, what is the probability of this event happening?

A) .20
B) 5/9
C) 4/9
D) .50
E) .80

Question 30

On one roll of a pair of dice, what is the probability of the points adding up to 5?

A) 1/3
B) 1/9
C) 1/12
D) 5/36
E) 2/9

Question 31

Event 3B
Given the following event:
Given two urns, one containing 1 yellow, 3 red, and 5 blue balls, and the other containing 4 yellow, 2 red, and 3 blue balls. A single ball is drawn from each.
Given Event 3B, what is the probability that one is red, the other is blue?

A) 2/3
B) 3/27
C) 77/81
D) 19/81
E) 1/3

Question 32

What is the probability of drawing either an ace or a king from a poker deck (no jokers) on a single draw?

A) 1/52
B) 1/26
C) 1/13
D) 2/13
E) 1/4

Question 33

To compute the probability of drawing a jack and a queen from a poker deck (without replacing the first card before drawing the second) the theory of probability that would likely be used is the:

A) Relative frequency theory.
B) Subjectivist theory.
C) Conditional theory.
D) Classical (a priori) theory.
E) Relativist theory.

Question 34

Event 2B
Given the following event:
Given an urn containing 2 green, 3 white, and 4 red balls. Two balls are drawn and the first ball is not replaced before the second is drawn.
Given Event 2B, what is the probability that the two balls are the same color?

A) 1/3
B) 2/9
C) 5/18
D) 1/6
E) 5/9

Question 35

Given an urn containing 4 red balls, 2 blue balls, and 3 yellow balls. What is the probability of drawing either a red ball or a blue ball on a single draw?

A) 2/3
B) 1/2
C) 8/9
D) 1/3
E) 4/9

Question 36

Event 3B
Given the following event:
Given two urns, one containing 1 yellow, 3 red, and 5 blue balls, and the other containing 4 yellow, 2 red, and 3 blue balls. A single ball is drawn from each.
Given Event 3B, what is the probability that at least one is either yellow or red?

A) 7/9
B) 5/27
C) 1/3
D) 2/3
E) 22/27

Question 37

What is the probability of getting at least 1 head on 5 successive tosses of a coin?

A) 3/4
B) 7/8
C) 31/32
D) 5/8
E) 15/16

Question 38

Given an urn containing 4 green balls and 5 orange balls. If two balls are drawn and the first ball is not replaced before the second is drawn, what is the probability that both balls are green?

A) 7/18
B) 1/6
C) 4/27
D) 7/17
E) 16/81

Question 39

If the odds of the Yankees beating the Red Sox are 5 to 3, what is the probability of this event happening?

A) 1/8
B) 5/8
C) 3/5
D) 3/8
E) 5/3

Question 40

Given an urn containing 3 red balls and 4 white balls. If two balls are drawn and the first ball is not replaced before the second is drawn, what is the probability that both balls are red?

A) 2/7
B) 7/12
C) 1/6
D) 1/7
E) 1/5

Question 41

Event 2A
Given the following event:
Given an urn containing 2 black, 3 yellow, and 5 orange balls. Two balls are drawn and the first ball is not replaced before the second is drawn.
Given Event 2A, what is the probability that the two balls are the same color?

A) 7/25
B) 19/45
C) 14/45
D) 8/25
E) 1/4

Question 42

Event 3A
Given the following event:
Given two urns, one containing 2 green, 3 yellow, and 5 pink balls, and the other containing 4 green, 2 yellow, and 4 pink balls. A single ball is drawn from each.
Given Event 3A, what is the probability that at least one is either green or yellow?

A) 4/5
B) 4/25
C) 1/5
D) 21/25
E) 67/100

Question 43

Event 3A
Given the following event:
Given two urns, one containing 2 green, 3 yellow, and 5 pink balls, and the other containing 4 green, 2 yellow, and 4 pink balls. A single ball is drawn from each.
Given Event 3A, what is the probability that one is green, the other is pink?

A) 1/4
B) 2/3
C) 8/25
D) 47/50
E) 7/25

Question 44

Event 2A
Given the following event:
Given an urn containing 2 black, 3 yellow, and 5 orange balls. Two balls are drawn and the first ball is not replaced before the second is drawn.
Given Event 2A, what is the probability that the first ball is orange and the second is yellow?

A) 1/25
B) 1/3
C) 3/20
D) 1/6
E) 1/5

Question 45

On one roll of a pair of dice, what is the probability of the points adding up to 6?

A) 5/36
B) 1/9
C) 1/6
D) 7/36
E) 2/9