Two sections of a senior probability course are being taught. From what she has heard about the two instructors listed, Francesca estimates that her chances of passing the course are 0.85 if she gets Professor X and 0.60 if she gets Professor Y. The section into which she is put is determined by the registrar. Suppose that her chances of being assigned to Professor X are four out of ten. Fifteen weeks later we learn that Francesca did, indeed, pass the course. What is the probability she was enrolled in Professor X's section?

Probability of Francesca passing the course by professor x is:-

Step-by-step explanation:

let the probability of Francesca passing the course by the professor x is p (A).

let the probability of Francesca passing the course by the professor y is p (B).

let the probability of assigning a professor x is p (E1).

let the probability of assigning a professor y is p (E2).

given,

p (A) = 0.85

p (B) = 0.60

p (E1) = 0.4

p (E2) = 1-0.4=0.6

the probability of Francesca pass the course with professor x is:-

= p (E1) * p (A) / p (E1) * p (A) + p (E2) * p (B)

= 0.4*0.85/0.4*0.85+0.6*0.60

= 0.485