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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:

Given that events A and B are independent with P(A)=0.25 P(A)=0.25 and P(B)=0.88 P(B)=0.88 , determine the value of P(AB) P(A \mid B) , rounding to the nearest thousandth, if necessary.\newlineAnswer:

Full solution

Q. Given that events A and B are independent with P(A)=0.25 P(A)=0.25 and P(B)=0.88 P(B)=0.88 , determine the value of P(AB) P(A \mid B) , rounding to the nearest thousandth, if necessary.\newlineAnswer:
  1. Understand Independent Events: Understand the concept of independent events. For two independent events AA and BB, the probability of AA occurring given that BB has occurred is the same as the probability of AA occurring by itself. This is because the occurrence of BB does not affect the probability of AA occurring. Mathematically, P(AB)=P(A)P(A|B) = P(A) for independent events.
  2. Apply Concept to Probabilities: Apply the concept to the given probabilities.\newlineSince events AA and BB are independent, we can directly use the probability of AA for P(AB)P(A\mid B).\newlineP(AB)=P(A)=0.25P(A\mid B) = P(A) = 0.25
  3. Round Answer if Necessary: Round the answer to the nearest thousandth if necessary.\newlineThe probability P(A)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.\newlineP(AB)=0.25P(A\mid B) = 0.25

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