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?

Question

Dickson

Mathematics

20 July, 16:25

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?

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Answers (1)

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Hadassah Park · Answer 1

the probability that Christine fails the course is 0.425

Step-by-step 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