Statistics Probability word problem

Question

A box contains a total of 100 CDs that were manufactured on two machines. Of them, 60 were manufactured on machine 1. Of the total CDs, 15 are defective. Of the 60 CDs that were manufactured on Machine 1, 9 are defective. Let A be the event that a randomly selected CD was manufactured on machine 1 and D be the event that a randomly selected CD is defective. Are events A and D independent or dependent?

 

(you need to show your work in details to receiv credit)

Answer 1

P(A and D) = P(A)P(D|A)

 

Is P(D | A) = P(D) ?

 

P(D|A) = 9/60 = 3/20

 

P(D) = 15/100 = 3/20

Answer 2

To show A and D are independent you need to show P(A∩D)=P(A)P(D).

 

The values of these three probabilities are actually given in the question. Can you figure them out?