Question

Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 65% chance that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 35%. There is only a 75% chance that she will find a tutor at such short notice.

What is the probability that Christine fails the course?

Answer 1

the probability that Christine fails the course is 0.425

Explanation:

A = Christine fails the course

B = Christine finds a tutor at such short notice

P(B) = 0.75

P(A|B) = 0.35

P(A|B') = 0.65

by total probability theorem

P(A) = P(A∩B) + P(A∩B')

by definition of intersection probability

P(A) = P(A|B)P(B) + P(A|B') P(B') = 0.35*0.75 + 0.65*(1-0.75)=0.425