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ruchik
Joined: 29 Nov 2018
Last visit: 09 Feb 2026
Posts: 91
Given Kudos: 57
Location: India
Concentration: Entrepreneurship, General Management
Schools: Sloan Fellows '22 IMD '22 (D)
GMAT 1: 730 Q50 V40
GPA: 3.99
WE:Engineering (Computer Hardware)
D
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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.
(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.
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ruchik
Joined: 29 Nov 2018
Last visit: 09 Feb 2026
Posts: 91
Own Kudos:
Given Kudos: 57
Location: India
Concentration: Entrepreneurship, General Management
Schools: Sloan Fellows '22 IMD '22 (D)
GMAT 1: 730 Q50 V40
GPA: 3.99
WE:Engineering (Computer Hardware)
18 Dec 2018, 20:52
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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
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
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
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Thank you for understanding, and happy exploring!
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