Suppose that P(A) = 1/3, P(B) = 1/3, and P(A ∩ Bc ) = 2/9. Are A and B independent? Why or why not?

The events A and B are not independent.

Step-by-step explanation:

Two events are independent, when the probability of one of them happening is not influenced by the fact that the other occurs -or does not occur-, considering that these events occur randomly. In other words, two events are independent if the result of the second event is not affected by the result of the first event.

The probability of the intersection of independent events is:

P(A∩B)=P(A)*P(B)

If A and B are independent events, the probability that both events occur is the product of the probabilities of the individual events, then they are independent events. The reciprocal is also true.

So, in this case, being:

P(A∩B)=1/3*1/3

So:

P(A∩B)=1/9

Being the data P (A∩B) = 2/9, if both events were independent P (A∩B) = 1/9. So the events A and B are not independent.

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