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

c. y = 1/4 x + 5

step-by-step explanation:

first, put the equation of the line on the graph into slope-intercept form

(y = mx + b):   y = -4x + 8

second, a perpendicular line has to have "an opposite/reciprocal slope" to the original slope. so, find the "m" value in your original equation (it's -4, right? )

original slope: m = -4   perpendicular slope: change the sign to its opposite and find the reciprocal ("flip" the number)

new slope is now positive (b/c the original slope was negative 4), and it's 1/4 (not the original slope of 4 or 4/1)