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 49% chance that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 19%. There is only a 59% 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)

Let

F = she fails
T = she finds a tutor

By Bayes\' Rule,

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

= 0.59*0.19 + (1-0.59)*(0.49)

= 0.3130 [answer]

************

b)

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

As

P(T n F) = P(T) P(F|T) = 0.59*0.19 = 0.1121

Then

P(T|F) = 0.1121/0.313 = 0.358146965 = 0.3581 [answer]