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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]

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24 Aug 2006, 23:08
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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

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Senior Manager
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24 Aug 2006, 23:15
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

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Director
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25 Aug 2006, 01:13
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

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25 Aug 2006, 06:32
I agree with E, I dont think we can assume its mutually exclusive or not.

Last edited by agsfaltex on 25 Aug 2006, 09:26, edited 1 time in total.

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Senior Manager
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25 Aug 2006, 07:14
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....

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Manager
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25 Aug 2006, 10:47
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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25 Aug 2006, 10:54
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?

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25 Aug 2006, 11:37
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.

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Manager
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25 Aug 2006, 12:33
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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26 Aug 2006, 07:50
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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26 Aug 2006, 07:50
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