SOLUTION: please solve this problem if P(A)=0.5, P(B)=0.6 and P(B/A)=0.9 find the probability that i)A & B both happens. ii)at least one of A & B happens. iii)only A happens.

Algebra ->  Probability-and-statistics -> SOLUTION: please solve this problem if P(A)=0.5, P(B)=0.6 and P(B/A)=0.9 find the probability that i)A & B both happens. ii)at least one of A & B happens. iii)only A happens.       Log On


   

Question 855770: please solve this problem if P(A)=0.5, P(B)=0.6 and P(B/A)=0.9 find the probability that i)A & B both happens. ii)at least one of A & B happens. iii)only A happens.
Found 2 solutions by stanbon, ewatrrr:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
please solve this problem if P(A)=0.5, P(B)=0.6 and P(B/A)=0.9 find the probability that
i)A & B both happens.
P(A AND B) = P(B|A)*P(A) = 0.9*0.5 = 0.45
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ii)at least one of A & B happens.
P(at least one of A or B) = 1 - P(neither A nor B) = 1-0.5*0.4 = 1-0.2 = 0.8
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iii)only A happens.
P(A) = 0.5
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Cheers,
Stan H.
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Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,

P(A)=0.5, P(B)=0.6 and P(B|A)=0.9   |Assume You mean conditional Probability

P(B|A) = P(B∩A)/P(A)= .9  ⇒ P(B∩A) = .9%2A.5+=+.45

P(A 0R B) = P(A) + P(B) - P(B∩A)  = .5 + .6 - .9 = .2

P(A) = .5