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Given that events A and B are independent with P(A)=0.55 and P(B)=0.72 determine the value of P(A∣B), rounding to the nearest thousandth

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This is a conditional probability problem

The conditional probability of A given B, denoted P(A|B), is the probability that event A has occurred in a trial of a random experiment for which it is known that event B has definitely occurred. It may be computed by means of the following formula:

To determine P(A|B)


P(A|B)=(P(AnB))/(P(B))
P(A|B)=(P(AnB))/(P(B))=\frac{P(A)\text{ x P(B)}}{P(B)}

Since P(A) = 0.55 and P(B)=0.72

So,


P(A|B)=\frac{P(A)\text{ x P(B)}}{P(B)}=\frac{0.55\text{ x 0.72}}{0.72}=0.55

P(A|B) =0.550 (To the nearest thousandth)

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