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There are three events A,B, and C, are they mutually

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Director
Joined: 18 Apr 2005
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There are three events A,B, and C, are they mutually [#permalink]  09 Jun 2005, 12:37
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There are three events A,B, and C, are they mutually exclusive?
1) P(A&B&C)=0.2
2) P(A) =0.2 and P(B)+P(C)=0.6

Last edited by sparky on 09 Jun 2005, 14:20, edited 1 time in total.
VP
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D)...mutually events cannot happen at the same time. so that two actions occur at the same time is 0 and that one or the other happens is 1.

1) the 3 events can happen at same time => suff

2) same as above

i am quite sure that its trickier ? but i am too tired...
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Director
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D is my pick too for the same reasoning as Chris
SVP
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Re: DS [#permalink]  09 Jun 2005, 19:39
A.
satement i is sufficient.
statement ii is not suff.
SVP
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Re: DS [#permalink]  09 Jun 2005, 21:20
Two events A and B are mutually exclusive if and only if P(A&B)=0

1) P(A&B&C)=0.2
Not mutually exclusive
Sufficient

2) P(A) =0.2 and P(B)+P(C)=0.6
Don't know anything about whether they are or are not mutually exclusive
Insufficient

A
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Director
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for mutually exclusive events, P(A) + P(B) + P(C) = 1 and P(A&B) = P(B&C) = P(A&C) = P(A&B&C) = 0

therefore, my AC would be D
Director
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Vithal wrote:
for mutually exclusive events, P(A) + P(B) + P(C) = 1 and P(A&B) = P(B&C) = P(A&C) = P(A&B&C) = 0

therefore, my AC would be D

P(A) + P(B) + P(C) = 0.8 not 1

also P(A) + P(B) + P(C) = 1 doesn't mean mutually exclusive, eg

P(A) + P(B) = 1- P(C), if P(C) is greater than 0, A and B aren't mutually exclusive
Director
Joined: 18 Apr 2005
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OA should be A, ditto H and HH

P(ABC) greater than zero automatically means they aren't mutually exclusive

but P(ABC) = 0 doesn't mean they are.

suppose P(AB) = 0 and P(ABC) >0

since ABC is a subset of AB, AC, and BC, it's not possible
Intern
Joined: 30 May 2005
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It should be A.

Statement 1 : sufficient as we all know. SO rule out option B, C and E.

Statement 2 : We have P(A) and P(B)+P(C). Since we dont have P(A or B or C) known so we can't conclude whether it is mutually exclusive. Hence B and D are ruled out.

Note : We can't make an assumption that P(A or B or C) =1 as Vithal has suggested.
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