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Re: Events A and B are independent and have equal probabilities of occurri
[#permalink]
18 Dec 2018, 19:52
Since A and B have equal probabilities of occurring (let’s call that probability p ), they also have equal probabilities of not occurring. The probability that neither of the events occurs is .25 (the complementary probability of .75, or 1 - .75). Therefore, the probability of A not occurring and the probability of B not occurring is .25. That means that (not p)(not p) = .25, or (not p)^2 = .25.
Take the square root of both sides to find that the probability of an event not occurring is .05. If we know the probability that an event will not occur, then we know the probability that it will occur. So Statement (1) is sufficient.
Statement (2): The probability that event A does not occur is simply 1 – p, so Statement (2) gives us p(1 – p) = .25. and factoring for two numbers that multiply to .25 and add to -1 (the implicit coefficient in front of p) gives us possible values for p: .5 So Statement (2) alone is sufficient.
Hence ans is D
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Re: Events A and B are independent and have equal probabilities of occurri [#permalink]