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14 October, 14:52

If A and B are independent events, which equation must be true?

A. P (B|A) = P (A)

B. P (B|A) = P (B)

C. P (B|A) = P (A) * P (B)

D. P (B|A) = P (A) + P (B)

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  1. 14 October, 14:56
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    P (B|A) = P (B)

    P (B|A) is the conditional probability of B knowing that A is happened. But since A and B are independent events, knowing that A already happened doesn't change anything.

    Here's an example: suppose that you have to flip a coin, and then toss a die. A is the event "the coin lands on tails" and B is the event "the die lands with the 5 face up".

    Now, we know that B has a probability of 1/6, because each of the six faces of the die will appears with the same probability.

    P (B|A) means "what's the probability that the die will land with the 5 face up, knowing that the coin landed on tail?"

    Well, it's always 1/6. Knowing that the coin landed on tail changes nothing about the die toss, because the two events are independent.
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