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A lot of components contains that are defective. Two components are drawn at random and tested. Let be the event that the first component drawn is defective, and let 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 . (b) Find . (c) Find . (d) Are and independent

User Robsn
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1 Answer

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19 votes

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.