Christine has always been weak in mathematics Based on her p

Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 57% chance that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 27%. There is only a 67% chance that she will find a tutor at such short notice.

What is the probability that Christine fails the course? (Round your answer to 4 decimal places.)

Christine ends up failing the course. What is the probability that she had found a tutor? (Round your answer to 4 decimal places.)

Solution

a)

By Bayes\' Rule,

P(fail) = P(tutor) P(fail|tutor) + P(no tutor) P(fail|no tutor)

= (0.67)(0.27) + (1-0.67)(0.57)

= 0.3690 [ANSWER]

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B)

P(tutor|fail) = P(tutor and fail)/P(fail)

As

P(tutor and fail) = P(tutor) P(fail|tutor) = 0.67(0.27) = 0.1809

Then

P(tutor|fail) = 0.1809/0.3690 = 0.4902 [ANSWER]