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 63% chance that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 33%. There is only a 73% chance that she will find a tutor at such short notice.

What is the probability that Christine fails the course?

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)

Let

T= finds tutor
F = fail

Thus,

P(F) = P(T) P(F|T) + P(T\') P(F|T\')

= 0.73*0.33 + (1-0.73)*0.63

= 0.411 [ANSWER]

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b)

P(T|F) = P(T)P(F|T)/P(F)

= 0.73*0.33/0.411

= 0.586131387 [ANSWER]