If two events A and B are independent, P(A∩B) equals what?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

If two events A and B are independent, P(A∩B) equals what?

Explanation:
Independence means the occurrence of one event doesn’t change the likelihood of the other. In that case, the chance that both events happen is the product of their individual probabilities. So P(A and B) = P(A) × P(B). This is the direct way to compute the intersection when A and B are independent. For example, if A has probability 0.5 and B has probability 0.5, then P(A and B) = 0.25. Note that independence also implies P(A|B) = P(A). So P(A∩B) can also be written as P(A|B)P(B) = P(A)P(B), but the simplest form for the intersection is P(A)P(B).

Independence means the occurrence of one event doesn’t change the likelihood of the other. In that case, the chance that both events happen is the product of their individual probabilities. So P(A and B) = P(A) × P(B). This is the direct way to compute the intersection when A and B are independent. For example, if A has probability 0.5 and B has probability 0.5, then P(A and B) = 0.25.

Note that independence also implies P(A|B) = P(A). So P(A∩B) can also be written as P(A|B)P(B) = P(A)P(B), but the simplest form for the intersection is P(A)P(B).

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