statistic question

Question

 A lot of 9 components contains 3

 that are defective. Two components are drawn at random and tested. Let A

 be the event that the first component drawn is defective, and let B

 be the event that the second component drawn is defective. Write your answer as a fraction or a decimal, rounded to four decimal places.

(a) Find 

PA

.(b) Find 

PB|A

.(c) Find 

PA and B

.(d) Are 

A and B independent? Explain.

Answer 1

There are 9 components with 3 of them defective (not working).

You are randomly selecting 2 components.

A = first component is defective

B = second component is defective

a.) P(A) = 3/9 = 1/3 or 0.3333 [the probability of drawing a first component is defective)

b.) P(B | A) = 2/8 = 1/4 or 0.25 [the probability of drawing a second component is defective, given that the first component is defective]

c.) P(A and B) = P(A) × P(B) = (1/3)*(1/4) = 1/12 or 0.08333

d.) Events A and B are independent because picking the first component will affect on picking the second component when there is no replacement. In this case, you don't put back the component in the original sample every time you draw the next component.