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Nums99
Joined: 12 Jan 2019
Last visit: 18 Mar 2022
Posts: 88
Given Kudos: 211
Location: India
Concentration: Finance, Technology
Schools: Rotman '23 Desautels '23 Alberta University
03 Aug 2019, 06:20
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
66% (01:57) correct
34%
(01:55)
wrong
based on 334
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When a random experiment is conducted, the probability that event A occurs is p, where 0 < p < 1. What is the value of p?
(1) When the random experiment is conducted 3 times, the probability that event A does not occur in any of the experiments is 0.512.
(2) When the random experiment is conducted 2 independent times, the ratio of the probability that event A occurs exactly once to the probability that event A occurs exactly twice is 2(1-p)/p
Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
EITHER statement BY ITSELF is sufficient to answer the question.
Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
(1) When the random experiment is conducted 3 times, the probability that event A does not occur in any of the experiments is 0.512.
(2) When the random experiment is conducted 2 independent times, the ratio of the probability that event A occurs exactly once to the probability that event A occurs exactly twice is 2(1-p)/p
Statement (1) BY ITSELF is sufficient to answer the question, but statement (2) by itself is not.
Statement (2) BY ITSELF is sufficient to answer the question, but statement (1) by itself is not.
Statements (1) and (2) TAKEN TOGETHER are sufficient to answer the question, even though NEITHER statement BY ITSELF is sufficient.
EITHER statement BY ITSELF is sufficient to answer the question.
Statements (1) and (2) TAKEN TOGETHER are NOT sufficient to answer the question, requiring more data pertaining to the problem.
03 Aug 2019, 11:42
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If p is the probability the event occurs, 1-p is the probability it does not. So the probability it does not occur on three experiments is (1-p)^3, and Statement 1 gives us the equation
(1 - p)^3 = 0.512
and we can take cube roots on both sides, and then solve for p (no need to do that work in DS but since 512 = 8^3, the cube root of 512/1000 is 8/10, so you'd find 1-p = 0.8 and p = 0.2), so Statement 1 is sufficient.
For Statement 2, the probability the event occurs twice in two tries is p^2. For the event to occur exactly once, it either occurs on the first try and not on the second, which happens with a probability of (p)(1-p), or it does not occur on the first try and does on the second, which also happens with a probability of (1-p)(p). Adding the two cases, the chance the event happens exactly once is 2(p)(1-p). So the ratio Statement 2 discusses, the ratio of the probability of one success to the probability of two successes, is equal to 2(p)(1-p) to p^2, or, dividing by p, is equal to 2(1-p) to p. But that's exactly what Statement 2 tells us. So Statement 2 is telling us something we could have figured out without using Statement 2 at all, and Statement 2 tells us no new information whatsoever -- Statement 2 is true for every possible value of p. So the answer is A.
(1 - p)^3 = 0.512
and we can take cube roots on both sides, and then solve for p (no need to do that work in DS but since 512 = 8^3, the cube root of 512/1000 is 8/10, so you'd find 1-p = 0.8 and p = 0.2), so Statement 1 is sufficient.
For Statement 2, the probability the event occurs twice in two tries is p^2. For the event to occur exactly once, it either occurs on the first try and not on the second, which happens with a probability of (p)(1-p), or it does not occur on the first try and does on the second, which also happens with a probability of (1-p)(p). Adding the two cases, the chance the event happens exactly once is 2(p)(1-p). So the ratio Statement 2 discusses, the ratio of the probability of one success to the probability of two successes, is equal to 2(p)(1-p) to p^2, or, dividing by p, is equal to 2(1-p) to p. But that's exactly what Statement 2 tells us. So Statement 2 is telling us something we could have figured out without using Statement 2 at all, and Statement 2 tells us no new information whatsoever -- Statement 2 is true for every possible value of p. So the answer is A.
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