Complete question is;
A lot of 10 components contains 4 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 P(A)
(b) Find P (B|A)
(c) Find P(A and B)
(d) Are A and B independent?
Answer:
A) P(A) = 0.4
B) P(B|A) = 1/3
C) P(A and B) = 2/15
D) They are not independent
Explanation:
We are told that A is the event that the first component drawn is defective, and B is the event that the second component drawn is defective.
A) Since 4 out of the 10 components are defective, then;
P(A) = 4/10 = 0.4
B) After taking 1 out of the 10, there will be 9 left and 3 defective ones left.
Thus; P(B|A) = 3/9 = 1/3
C) P(A and B) = P(A) × P(B|A)
Thus;
P(A and B) = 4/10 × 1/3
P(A and B) = 4/30 = 2/15
D) They are not independent because B can't be done until A is done whereby the first component is drawn.