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Roll two fair dice. Each die has six faces. • Let A be the event that either a 3 or 4 is rolled first, followed by an even number. • Let B be the event that the sum of the two rolls is at most 7.

Roll two fair dice. Each die has six faces. • Let A be the event that either a 3 or 4 is rolled first, followed by an even number. • Let B be the event that the sum of the two rolls is at most 7.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Roll two fair dice. Each die has six faces.

• Let A be the event that either a 3 or 4 is rolled first, followed by an even number.

• Let B be the event that the sum of the two rolls is at most 7. 

Refer to the attachment for the questions.

O Part (d) In words, explain what "P(A | B)" represents. O PLA | B) represents the probability the sum of the dice is at most 7, given that the second die is an even number. O PIA | B) represents the probability that the sum of the dice is at most 7, given that the first die is a 3 or 4 and the second die is an even number. O PIA | B) represents the probability of rolling a 3 or 4 on the first die, followed by an even number, given that the sum of the dice is at most 7. O PLA | B) represents the probability of rolling a 3 or 4 on the first die, given that the second die is an even number. Find P(A | B). (Enter your answer as a fraction.) P(A | B) = O Part (e) Are A and B mutually exclusive events? Explain your answer. O The events are not mutually exclusive. Rolling 4, 6 is an outcome in event A but not in event B. O The events are mutually exclusive. Rolling 3, 2 is an outcome in event A and also an outcome in event B. O The events are mutually exclusive. Rolling 4, 6 is an outcome in event A but not in event B. O The events are not mutually exclusive. Rolling 3, 2 is an outcome in event A and also an outcome in event B. O Part (f) Are A and B independent events? Explain your answer. O Events A and B are independent because they are mutually exclusive. O Events A and B are dependent because they have outcomes in common. O Events A and B are independent because the roll of one die has no effect on the outcome of rolling a second die. O Events A and B are dependent because the probability of event A happening is affected by whether event B has happened.
Transcribed Image Text:O Part (d) In words, explain what "P(A | B)" represents. O PLA | B) represents the probability the sum of the dice is at most 7, given that the second die is an even number. O PIA | B) represents the probability that the sum of the dice is at most 7, given that the first die is a 3 or 4 and the second die is an even number. O PIA | B) represents the probability of rolling a 3 or 4 on the first die, followed by an even number, given that the sum of the dice is at most 7. O PLA | B) represents the probability of rolling a 3 or 4 on the first die, given that the second die is an even number. Find P(A | B). (Enter your answer as a fraction.) P(A | B) = O Part (e) Are A and B mutually exclusive events? Explain your answer. O The events are not mutually exclusive. Rolling 4, 6 is an outcome in event A but not in event B. O The events are mutually exclusive. Rolling 3, 2 is an outcome in event A and also an outcome in event B. O The events are mutually exclusive. Rolling 4, 6 is an outcome in event A but not in event B. O The events are not mutually exclusive. Rolling 3, 2 is an outcome in event A and also an outcome in event B. O Part (f) Are A and B independent events? Explain your answer. O Events A and B are independent because they are mutually exclusive. O Events A and B are dependent because they have outcomes in common. O Events A and B are independent because the roll of one die has no effect on the outcome of rolling a second die. O Events A and B are dependent because the probability of event A happening is affected by whether event B has happened.
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