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Updated on: 09 Feb 2026, 23:43
Originally posted by goodyear2013 on 09 Jan 2014, 17:11.
Last edited by Bunuel on 09 Feb 2026, 23:43, edited 1 time in total.
Last edited by Bunuel on 09 Feb 2026, 23:43, edited 1 time in total.
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E
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:
54% (01:25) correct
46%
(01:05)
wrong
based on 723
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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.
(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.
Show Spoiler 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
MY DOUBT:
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.
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
MY DOUBT:
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.
09 Jan 2014, 21:30
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goodyear2013
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.
General Discussion
13 Jul 2015, 06:10
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VeritasPrepKarishma
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
