If the probability of A union B is 2/3, the probability of A intersection B is...

Question

Question

If the probability of A union B is 2/3, the probability of A intersection B is 1/3, and the probability of A is 1/2, then

	a.	the probability of B is 5/6
	b.	the probability of A given B is 3/5
	c.	A and B are not independent
	d.	All of the above

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Answer 1

Answer #1

P(A union B) = P(A) +P(B) - P(A intersection B)

2/3 = 1/2 + P(B) - 1/3

2/3 -1/2 +1/3 = P(B)

P(B) =( 4-3 +2)/6 = 3/6 = 1/2.

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

1/3 = 1/2 P(A/B)

P(A/B) = 2/3

Probability of A given B = 2/3

A and B are not independent because if A and B are independent ,then P(A intersection B) should be equal to P(A) multiplied by P(B).

Hence, option(C) is correct.

Answer 2

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