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# The events A, B, and C are independent. What is the probability that

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Senior Manager
Joined: 21 Oct 2013
Posts: 435
The events A, B, and C are independent. What is the probability that [#permalink]

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09 Jan 2014, 17:11
2
6
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Difficulty:

55% (hard)

Question Stats:

50% (01:29) correct 50% (00:32) wrong based on 283 sessions

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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.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8100
Location: Pune, India
Re: The events A, B, and C are independent. What is the probability that [#permalink]

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09 Jan 2014, 21:30
6
1
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.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Intern Joined: 09 Dec 2014 Posts: 46 GMAT 1: 600 Q42 V32 GMAT 2: 710 Q48 V38 GPA: 3.7 Re: The events A, B, and C are independent. What is the probability that [#permalink] ### Show Tags 13 Jul 2015, 06:10 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 Manager Joined: 13 Feb 2011 Posts: 95 Re: The events A, B, and C are independent. What is the probability that [#permalink] ### Show Tags 17 Sep 2015, 15:21 2 1 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, $$1-4/7$$ 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. Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8100 Location: Pune, India Re: The events A, B, and C are independent. What is the probability that [#permalink] ### Show Tags 17 Sep 2015, 23:11 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: The events A, B, and C are independent. What is the probability that [#permalink]

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20 Jan 2018, 11:56
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Re: The events A, B, and C are independent. What is the probability that   [#permalink] 20 Jan 2018, 11:56
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