Beth is taking an eleven question multiple-choice test for which each question has three answer choices, one of which is correct.Beth decides on answers by rolling a fair die and marking the first answer choice if the die shows 1 or 2 ,the second if the die shows 3 or 4,and the third if the die shows 5 or 6. Find the probability of the stated event. Exactly five correct answers. The probability of Beth getting exactly five correct answers is

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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Beth is taking an eleven question multiple-choice test for which each question has three answer choices, one of which is correct.Beth decides on answers by rolling a fair die and marking the first answer choice if the die shows 1 or 2 ,the second if the die shows 3 or 4,and the third if the die shows 5 or 6. Find the probability of the stated event. Exactly five correct answers. The probability of Beth getting exactly five correct answers is

Expert Solution
Step 1

There are 6 outcomes on a fair 6-sided die. 

The probability of each outcome is= 16

So the probability of selecting the first choice=P(1)+P(2)=16+16=13

the probability of selecting the second choice=P(3)+P(4)=16+16=13

the probability of selecting the third choice=P(5)+P(6)=16+16=13

 

 

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