Given that events A and B are independent with P(A)=0.25 and P(B)=0.88, determine the value of P(A∣B), rounding to the nearest thousandth, if necessary.Answer:
Q. Given that events A and B are independent with P(A)=0.25 and P(B)=0.88, determine the value of P(A∣B), rounding to the nearest thousandth, if necessary.Answer:
Understand Independent Events: Understand the concept of independent events. For two independent events A and B, the probability of A occurring given that B has occurred is the same as the probability of A occurring by itself. This is because the occurrence of B does not affect the probability of A occurring. Mathematically, P(A∣B)=P(A) for independent events.
Apply Concept to Probabilities: Apply the concept to the given probabilities.Since events A and B are independent, we can directly use the probability of A for P(A∣B).P(A∣B)=P(A)=0.25
Round Answer if Necessary: Round the answer to the nearest thousandth if necessary.The probability P(A) is already given to two decimal places, which is more precise than rounding to the nearest thousandth. Therefore, no additional rounding is necessary.P(A∣B)=0.25
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