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If X and Y are two events with probabilities P(X) = 1/3, P(X given Y) = 1/2, and P(Y given X) = 2/5, what is true?

1. The probability of both X and Y occurring is 1/5.
2. The probability of Y occurring is 4/15.
3. The probability of either X or Y occurring is 2/5.
4. The probability of X not occurring given that Y has not occurred is 1/2.

Correct answer: The probability of Y occurring is 4/15.

Solution

Using the given probabilities and conditional probabilities, we can calculate the probability of Y occurring, which is 4/15, making option B the correct statement.

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