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P(A)=0.6, P(B)=0.5. What is the largest possible probability

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HongHu
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P(A)=0.6, P(B)=0.5. What is the largest possible probability [#permalink] New post   24 Jan 2005, 22:29
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P(A)=0.6, P(B)=0.5. What is the largest possible probability of both A and B not happening?



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Re: P(A)=0.6, P(B)=0.5. What is the largest possible probability [#permalink] New post   25 Jan 2005, 00:23
Is it 0.4*0.5 = 0.2 ?
May be I am not understanding the concept of largest possible probability !
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Re: P(A)=0.6, P(B)=0.5. What is the largest possible probability [#permalink] New post   25 Jan 2005, 10:29
OA is 0.4.

I suppose it is because A and B may not be independent to each other.
I did this one wrong too.
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Re: P(A)=0.6, P(B)=0.5. What is the largest possible probability [#permalink] New post   25 Jan 2005, 10:30
HongHu wrote:
OA is 0.4.

I suppose it is because A and B may not be independent to each other.
I did this one wrong too.


How does the calculation go in the explanation ?
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Re: P(A)=0.6, P(B)=0.5. What is the largest possible probability [#permalink] New post   25 Jan 2005, 10:38
There's no explanation so this is only my understanding:

Possibility of A not occuring: 1-P(A)=0.4
Possibility of B not occuring: 1-P(B)=0.5

If they are independent, then possibility of both of them not occuring would be (1-P(A))(1-P(B))=0.2

However if B is dependent to A, say B can only happen when A happens, then the possibility of both of them not occuring would be equal to the possibility of A not occuring, which is 0.4.
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Re: P(A)=0.6, P(B)=0.5. What is the largest possible probability [#permalink] New post   25 Jan 2005, 10:45
HongHu wrote:
There's no explanation so this is only my understanding:

Possibility of A not occuring: 1-P(A)=0.4
Possibility of B not occuring: 1-P(B)=0.5

If they are independent, then possibility of both of them not occuring would be (1-P(A))(1-P(B))=0.2

However if B is dependent to A, say B can only happen when A happens, then the possibility of both of them not occuring would be equal to the possibility of A not occuring, which is 0.4.


Reverse A and B in ur explnation then prob of B not happening is 0.5...stem asks highest prob so ...in that case 0.5 shud be the ans not 0.4 :?:
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Re: P(A)=0.6, P(B)=0.5. What is the largest possible probability [#permalink] New post   25 Jan 2005, 11:52
But A will happen 60% of time so it can't be possible that both A and B not happen half of the time.
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Re: P(A)=0.6, P(B)=0.5. What is the largest possible probability [#permalink] New post   01 Feb 2005, 23:13
The possibility of A AND B not happening is either A OR B not happening.

1-A or 1-B. Greatest possiblity is 1-A =.4
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Re: P(A)=0.6, P(B)=0.5. What is the largest possible probability [#permalink] New post   02 Feb 2005, 05:35
rc1979 wrote:
The possibility of A AND B not happening is either A OR B not happening.

1-A or 1-B. Greatest possiblity is 1-A =.4


You solution looks interesting but it's not clear.
I got 0.2.
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Re: P(A)=0.6, P(B)=0.5. What is the largest possible probability [#permalink] New post   02 Feb 2005, 08:42
If they are independent to each other, than you get 0.2. Otherwise, max can be 0.4.
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Re: P(A)=0.6, P(B)=0.5. What is the largest possible probability [#permalink] New post   04 Feb 2005, 13:15
whenever the question of max comes it implies possibility of dependence and one can follow baye's theorem too.
Anirban



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