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The events A, B, and C are independent. What is the probability that [#permalink]
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09 Jan 2014, 16:11
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The events A, B, and C are independent. What is the probability that all 3 events A, B, and C occur? (1) The probability that event A occurs is 1/3. (2) The probability that neither of the events B and C occur is 4/7. OE (1): Given no probabilities of event B or C Insufficient (2): Given no probability that event A occurs Insufficient Combined: From (1), we have the probability that event A occurs. (2) says that probability that neither of the events B and C occurs is 4/7. So, the probability that at least one of the events B and C occurs is 1 – 4/7 = 3/7. Note that the probability of "at least one" of the 2 events occurring is distinct from the probability of both occurring. "At least one" means either B, or C, or both occur. cannot use this information to find probability of both B and C occurring, so cannot find probability of all 3 events occurring. Insufficient Hi, I think this question is overlapping sets with 3 group. I can get the correct answer, but I want to clarify how combined statements work, please.
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Re: The events A, B, and C are independent. What is the probability that [#permalink]
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09 Jan 2014, 20:30
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goodyear2013 wrote: The events A, B, and C are independent. What is the probability that all 3 events A, B, and C occur? (1) The probability that event A occurs is 1/3. (2) The probability that neither of the events B and C occur is 4/7. OE (1): Given no probabilities of event B or C Insufficient (2): Given no probability that event A occurs Insufficient Combined: From (1), we have the probability that event A occurs. (2) says that probability that neither of the events B and C occurs is 4/7. So, the probability that at least one of the events B and C occurs is 1 – 4/7 = 3/7. Note that the probability of "at least one" of the 2 events occurring is distinct from the probability of both occurring. "At least one" means either B, or C, or both occur. cannot use this information to find probability of both B and C occurring, so cannot find probability of all 3 events occurring. Insufficient Hi, I think this question is overlapping sets with 3 group. I can get the correct answer, but I want to clarify how combined statements work, please. What is the probability of three independent events occurring together? It is the product of their probabilities. P(A and B and C) = P(A) * P(B) * P(C) Think here of three overlapping sets. This is the region where all three overlap. Again, since B and C are independent P(B and C) = P(B) * P(C) This is the region where B and C overlap. Statement 1 gives us P(A). Statement 2 gives us that P(B or C) = 1  4/7 = 3/7. If we imagine only B and C, this is the total region inside the two circles including the overlap. What we actually needed was the region of overlap of B and C i.e. P(B and C). Hence both statements together are not sufficient.
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Re: The events A, B, and C are independent. What is the probability that [#permalink]
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13 Jul 2015, 05:10
VeritasPrepKarishma wrote: goodyear2013 wrote: The events A, B, and C are independent. What is the probability that all 3 events A, B, and C occur? (1) The probability that event A occurs is 1/3. (2) The probability that neither of the events B and C occur is 4/7. OE (1): Given no probabilities of event B or C Insufficient (2): Given no probability that event A occurs Insufficient Combined: From (1), we have the probability that event A occurs. (2) says that probability that neither of the events B and C occurs is 4/7. So, the probability that at least one of the events B and C occurs is 1 – 4/7 = 3/7. Note that the probability of "at least one" of the 2 events occurring is distinct from the probability of both occurring. "At least one" means either B, or C, or both occur. cannot use this information to find probability of both B and C occurring, so cannot find probability of all 3 events occurring. Insufficient Hi Hi, I think this question is overlapping sets with 3 group. I can get the correct answer, but I want to clarify how combined statements work, please. What is the probability of three independent events occurring together? It is the product of their probabilities. P(A and B and C) = P(A) * P(B) * P(C) Think here of three overlapping sets. This is the region where all three overlap. Again, since B and C are independent P(B and C) = P(B) * P(C) This is the region where B and C overlap. Statement 1 gives us P(A). Statement 2 gives us that P(B or C) = 1  4/7 = 3/7. If we imagine only B and C, this is the total region inside the two circles including the overlap. What we actually needed was the region of overlap of B and C i.e. P(B and C). Hence both statements together are not sufficient. Hi Karishma, In the question it says that neither of the events B and C occur is 4/7 ( This would basically mean probability of event B not happening and probability of event C not happening is 4/7, right? ) . So when we convert it to the opposite should we take it as probability of event B happening or probability of event C happening? Is my logic correct? Thanks in advance, Ray



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Re: The events A, B, and C are independent. What is the probability that [#permalink]
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17 Sep 2015, 14:21
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Alchemist14 wrote: In the question it says that neither of the events B and C occur is 4/7 ( This would basically mean probability of event B not happening and probability of event C not happening is 4/7, right? ) . So when we convert it to the opposite should we take it as probability of event B happening or probability of event C happening?
Is my logic correct?
Thanks in advance, Ray Probability that NEITHER B NOR C occurs = \(4/7\). However, \(14/7\) is not the probability of BOTH B AND C occurring, rather it's the probability of AT LEAST 1 of them occurring (this includes three cases  Only B, Only C, and BOTH B and C). Therefore, as we do not know the exact probability of occurrence of BOTH B and C, choice (2) doesn't helps.



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Re: The events A, B, and C are independent. What is the probability that [#permalink]
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17 Sep 2015, 22:11
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Alchemist14 wrote: VeritasPrepKarishma wrote: goodyear2013 wrote: The events A, B, and C are independent. What is the probability that all 3 events A, B, and C occur? (1) The probability that event A occurs is 1/3. (2) The probability that neither of the events B and C occur is 4/7. OE (1): Given no probabilities of event B or C Insufficient (2): Given no probability that event A occurs Insufficient Combined: From (1), we have the probability that event A occurs. (2) says that probability that neither of the events B and C occurs is 4/7. So, the probability that at least one of the events B and C occurs is 1 – 4/7 = 3/7. Note that the probability of "at least one" of the 2 events occurring is distinct from the probability of both occurring. "At least one" means either B, or C, or both occur. cannot use this information to find probability of both B and C occurring, so cannot find probability of all 3 events occurring. Insufficient Hi Hi, I think this question is overlapping sets with 3 group. I can get the correct answer, but I want to clarify how combined statements work, please. What is the probability of three independent events occurring together? It is the product of their probabilities. P(A and B and C) = P(A) * P(B) * P(C) Think here of three overlapping sets. This is the region where all three overlap. Again, since B and C are independent P(B and C) = P(B) * P(C) This is the region where B and C overlap. Statement 1 gives us P(A). Statement 2 gives us that P(B or C) = 1  4/7 = 3/7. If we imagine only B and C, this is the total region inside the two circles including the overlap. What we actually needed was the region of overlap of B and C i.e. P(B and C). Hence both statements together are not sufficient. Hi Karishma, In the question it says that neither of the events B and C occur is 4/7 ( This would basically mean probability of event B not happening and probability of event C not happening is 4/7, right? ) . So when we convert it to the opposite should we take it as probability of event B happening or probability of event C happening? Is my logic correct? Thanks in advance, Ray Yes, 4/7 is the probability that both B and C do not happen. So 1  4/7 will be the probability that at least one of them does take place. This is P(B or C) i.e. probability that B happens or C happens or both happen.
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