Answer to Question #151543 in Statistics and Probability for Winfred

Question

The probability that a student passing a CAT is ¾, if he pass the CAT, the probability of getting grade A finally is 5/6. If he fails the probability of getting on A would be 1/5. If a student gets a grade A what is the probability that he passed the CAT

Answer 1

The probability P₁ of the event that a student passes CAT and gets a grade A is:

P₁= 3/4*5/6 = 5/8

The probability P₂ of the event that a student does not pass CAT and gets a grade A is:

P₂ = 1/4*1/5 = 1/20

The probability P₃ of the event that a student gets a grade A is:

P₃ = P₁+ P₂ = 5/8 + 1/20 = 27/40

The probability P₄ of the event that a student passed CAT if he gets a grade A is:

P₄ = P₁ / P₃= (5/8) / (27/40) = 25/27