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Probability

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Probability

by JANJAN » Sun Feb 13, 2011 10:31 am
Let A and B be two events in a sample space. Suppose that P(A) = 0.4 and P(A∩B) = 0.7. Let P (B) =p.
(a) Find the value of p for which A and B are mutually exclusive.
(b) Find the value of p for which A and B are independent.

Can anyone guide me on how to approach this problem? Thank you
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by maihuna » Sun Feb 13, 2011 10:48 am
I think u have AUB and not A&B and P(A&B) cant be more than either of A or B

AUB = A+B-A&B, short cut used to avoid typing, p understood, and & means Intersection

For Mutual Exclusive one, A&B=0, so B = AUB-A = 0.7-0.4 = 0.3

For Independent Event : P(A and B) = P(A) · P(B) so b can be found
Charged up again to beat the beast :)
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by JANJAN » Sun Feb 13, 2011 11:11 am
maihuna wrote:I think u have AUB and not A&B and P(A&B) cant be more than either of A or B

AUB = A+B-A&B, short cut used to avoid typing, p understood, and & means Intersection

For Mutual Exclusive one, A&B=0, so B = AUB-A = 0.7-0.4 = 0.3

For Independent Event : P(A and B) = P(A) · P(B) so b can be found
This is why I am stuck. Those are the conditions given. P(A)=o.4, P(A&B)=0.7. How do I determine the value of B whether independent or mutually exclusive? I am soooooo stuck!
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