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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: 411
The events A, B, and C are independent. What is the probability that  [#permalink]

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09 Jan 2014, 17:11
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Difficulty:

55% (hard)

Question Stats:

56% (01:25) correct 44% (01:01) wrong based on 348 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: 9705
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

##### General Discussion
Intern
Joined: 09 Dec 2014
Posts: 44
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]

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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?

Ray
Manager
Joined: 13 Feb 2011
Posts: 79
Re: The events A, B, and C are independent. What is the probability that  [#permalink]

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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?

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: 9705
Location: Pune, India
Re: The events A, B, and C are independent. What is the probability that  [#permalink]

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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?

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

Intern
Joined: 07 Jul 2018
Posts: 44
Re: The events A, B, and C are independent. What is the probability that  [#permalink]

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23 Jan 2019, 02:20
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.

Hi,

Solving it pure algebraically,
We are given P(B' AND C')

P(B' AND C') = 1 - P(B AND C)

So we obtain P(B and C) from it, where am I going wrong?

Thanks.
Re: The events A, B, and C are independent. What is the probability that   [#permalink] 23 Jan 2019, 02:20
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