Question

A lot of 1500 components contains 200 that are defective. Two components are drawn at random and tested. Let A be the event that the first component drawn in defective, let B be the event that the second component drawn is defect, let C be the event that the first component drawn is not defective.

E. Find P(B|C)

F. Are A and B independent?

G. Find P(A ∪ B^c)

H. Find (A ∩ C)

Answer 1

P(A) = 200/1500 = 2/15

P(B) = 2/15

P(C) = 1 - 2/15 = 13/15

E. P(B | C) = P(B & C)/P(C) [Bayes' Theorem]

1300/1500 x 200/1499 / (1300/1500)

= 200/1499

= 0.1334

F. No

P(B) = 200/1500

P(B | A) = 199/1500

P(B) P(B | A)

So, A and B are not independent

G. P(A U B^c) = P(A) + P(B^c) - P(A B^c)

= 2/15 + 13/15 - 2/15x1300/1499

= 0.8844

H. P(A C) = 0