Question

Christine has always been weak in mathematics. Based on her performance prior to the final exam in Calculus, there is a 43% chance that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 13%. There is only a 53% chance that she will find a tutor at such short notice. a. What is the probability that Christine fails the course? (Round your answer to 4 decimal places.) Probability b. Christine ends up failing the course. What is the probability that she had found a tutor? (Round your answer to 4 decimal places.) Probability ________

Answer 1

a) Pr. that Christine fails the course = 0.271

b) Probability that she finds a tutor given she ends failing the course or failed = 0.2542

Explanation:

With Tutor Without Tutor

Fail 13% = 0.13 43% = 0.43

Find Tutor 53% = 0.53

a) Probability that Christine fails the course = Pr. that (she fails with tutor) × Pr. (that she fails without tutor)

Pr. that Christine fails the course = (0.53 × 0.13) + ( 0.47 × 0.43)

Pr. that Christine fails the course = 0.0689 + 0.2021

Pr. that Christine fails the course = 0.271

b)

Probability that she finds a tutor given she ends failing the course or failed =
`(0.53*0.13)/(0.271)`

= 0.2542