In which of the following are the events A and B not independent?

Question

I. P(A)=1/4, P(B)=1/5, p(AnB)=1/9

II. P(A)=0.2,P(B)=0.5, P(AnB)=0.01

III.P(A)=1/2,P(B)=3/5,P(AnB)=3/10

Explain your answer

Answer 1

When P(A)*P(B)=P(A^B) where ^ represents "and" or intersection, the probabilities are independent.

In (I), 1/4 * 1/5 = 1/20 ≠ 1/9 so the probabilities are not independent. In (II) and (III) the probabilities are independent.

Comments

Thanks, but 0.2*0.5 #0.01

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Sorry, you are right! So II, too, is an example of non-independence.

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Thanks

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I hope that's right. It's made me think twice about the problem!