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# What is the probability that events A and B both occur? (1)

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Manager
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What is the probability that events A and B both occur? (1) [#permalink]  24 Aug 2006, 22:08
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What is the probability that events A and B both occur?

(1) the probability that event A occurs is 0.8
(2) the probability that event B occurs is 0.6
Senior Manager
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Straight E

P(A or B) = P(A) + P(B) - P(A and B)

ST 1 by itself is INSUFF

ST 2 by itself is INSUFF

Combining the two still does not give us P(A and B). Hence E
Director
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I would say that the prob for both events to occur is 0,8*0,6=0,48.
The problem is if both events may occur at the same time , in other words if they are not mutually exclusive
Senior Manager
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I agree with E, I dont think we can assume its mutually exclusive or not.

Last edited by agsfaltex on 25 Aug 2006, 08:26, edited 1 time in total.
Senior Manager
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BG wrote:
I would say that the prob for both events to occur is 0,8*0,6=0,48.
The problem is if both events may occur at the same time , in other words if they are not mutually exclusive

But the problem here is that it does not state if they are mutually exclusive events or not... If so then only prob for both is 0....
Manager
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gmatornot wrote:
Straight E

P(A or B) = P(A) + P(B) - P(A and B)

ST 1 by itself is INSUFF

ST 2 by itself is INSUFF

Combining the two still does not give us P(A and B). Hence E

Since there are only 2 events, P(A or B) = 1
Thus, from (1) + (2), we can obtain P(A and B).
Hence the answer should be (C), right ?
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Prashrash.

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prashrash wrote:
gmatornot wrote:
Straight E

P(A or B) = P(A) + P(B) - P(A and B)

ST 1 by itself is INSUFF

ST 2 by itself is INSUFF

Combining the two still does not give us P(A and B). Hence E

Since there are only 2 events, P(A or B) = 1
Thus, from (1) + (2), we can obtain P(A and B).
Hence the answer should be (C), right ?

According to your explanation, since P(A or B)=1, P(A and B) = 0.4. What if A and B are mutually exclusive (which we dont know) ? Then P(A and B) would have to be 0. So you see, you have two answers: 0.4 and 0. Not possible, is it?
VP
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Got to be E...

P(A&B) = P(A) + P(B) - P(A or B)

Did not give us P(A or B)... don't know if mutually exclusive. Therefore E.
Manager
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oh yeah! read the qn and assumed that A and B can't be mutually exclusive events! Pure dumbness on my part.
Agreed E.
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Prashrash.

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Good discussion. I was stumped, honestly, and quick to jump at C. Agree with E.

To reiterate:

In general:-

P(A OR B) = P(A) + P(B) - P(A&B)

2 events are mutually exclusive if they cannot happen together i.e. P (A&B) = 0.

If so, then

P(A OR B) = P(A) + P(B)
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