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 66% chance that she will fail the course if she does not have a tutor. With a tutor, her probability of failing decreases to 36%. There is only a 76% 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

PART A:
We can write the given details.

24 % No tutor(100-76) - 66% chance of fail with no tutor.

66/10=0.66 chance of fail with no tutor.

1-0.66= 0.34 chance of pass with no tutor.

36%=0.36 =chance of fail with tutor.

1-0.36=0.64 = Chance of pass with Tutor.

There are two ways she can fail:
No tutor and fail (0.24 * 0.66)
Tutor and fail (0.76 * 0.36)

Add these together:
P(fail) = (0.24 * 0.66) + (0.76 * 0.36)
P(fail)= 0.432

P(fail)= 43.2%

PART B:

The chance she failed with a tutor is:
(0.76 * 0.36) = 0.2736

We want the probability that she had a tutor given she failed. We just need to divide this result by the probability of failing either way (already figured in PART A).

Therefore, the conditional probability she found a tutor, given she failed is:
P(tutor | failed) = P(tutor and failed) / P(failed)
= 0.2736 / 0.432
=0.633

63.3%