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Events A and B are independent and have equal probabilities of occurri

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Events A and B are independent and have equal probabilities of occurri  [#permalink]

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New post Updated on: 18 Dec 2018, 20:58
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Events A and B are independent and have equal probabilities of occurring. What is the probability that event A occurs?

(1) The probability that at least one of events A and B occurs is .75.
(2) The probability that event B occurs and event A does not is .25.

Originally posted by ruchik on 18 Dec 2018, 19:45.
Last edited by Bunuel on 18 Dec 2018, 20:58, edited 2 times in total.
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Joined: 29 Nov 2018
Posts: 47
Location: India
Concentration: Entrepreneurship, General Management
GPA: 3.99
WE: Engineering (Computer Hardware)
Re: Events A and B are independent and have equal probabilities of occurri  [#permalink]

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New post 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
GMAT Club Bot
Re: Events A and B are independent and have equal probabilities of occurri &nbs [#permalink] 18 Dec 2018, 19:52
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Events A and B are independent and have equal probabilities of occurri

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