A lot of 1000 components contains 300 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.

a. Find P(A).

b. Find P(B|A) .

c. Find P(A ∩ B).

d. Find P(Ac ∩ B).

e. Find P(B) .

f. Find P(A|B).

g. Are Aand B independent? Is it reasonable to treat A and B as though they were independent? Explain.

Answer :

Step 1 of 8 :

Given, 300 are defective in a lot of 1000 components. Two components are drawn at random and tested.

Let A be the event that the first component drawn is defective and B be the event that the second component drawn is defective.

Step 2 of 8 :

The claim is to find the the probability of first component is defectiveThat is P(A)

Where, A is the event that the first component drawn is defective.

We have 1000 components, in that 300 are defectives.

then, P(first component is defective) =

=

=

Therefore, P(A) = 3/10.

Step 3 of 8 :

b)

the claim is to find the P(B/A)

If A occurs, then there are 999 components remaining.

In remaining 999 components 299 are defectives

Then, P(B/A) =

= .

Therefore, P(B/A) = .

Step 4 of 8 :

c)

The claim is to find P()

We know that

P() = P(A) P(B/A)

= () ()

=

Therefore, P() = .