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

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

Step-by-step 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 =

= 0.2542

The amount is $8358.7 and the interest is $3858.7.

Explanation:

STEP 1: To find amount we use formula:

A = total amount

P = principal or amount of money deposited,

r = annual interest rate

n = number of times compounded per year

t = time in years

Step-by-step explanation: