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A First Course in Probability | 9th Edition | ISBN: 9780321794772 | Authors: Sheldon Ross
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A recent college graduate is planning to take the first

Chapter 3, Problem 12P

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QUESTION:

Problem 12P

A recent college graduate is planning to take the first three actuarial examinations in the coming summer. She will take the first actuarial exam in June. If she passes that exam, then she will take the second exam in July, and if she also passes that one, then she will take the third exam in September. If she fails an exam, then she is not allowed to take any others. The probability that she passes the first exam is .9. If she passes the first exam, then the conditional probability that she passes the second one is .8, and if she passes both the first and the second exams, then the conditional probability that she passes the third exam is .7.

(a) What is the probability that she passes all three exams?

(b) Given that she did not pass all three exams, what is the conditional probability that she failed the second exam?

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QUESTION:

Problem 12P

A recent college graduate is planning to take the first three actuarial examinations in the coming summer. She will take the first actuarial exam in June. If she passes that exam, then she will take the second exam in July, and if she also passes that one, then she will take the third exam in September. If she fails an exam, then she is not allowed to take any others. The probability that she passes the first exam is .9. If she passes the first exam, then the conditional probability that she passes the second one is .8, and if she passes both the first and the second exams, then the conditional probability that she passes the third exam is .7.

(a) What is the probability that she passes all three exams?

(b) Given that she did not pass all three exams, what is the conditional probability that she failed the second exam?

ANSWER:

Step 1 of 3

Let us consider be the event that the actuarial exam is passed. Then the given probabilities can be expressed as:

Here our goal is:

a). We need to find the probability that she passes all three exams.

b). We need to find the conditional probability that she failed the second exam.

 

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