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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 $P(A)=0.25$ and $P(B)=0.88$ , determine the value of $P(A \mid B)$ , rounding to the nearest thousandth, if necessary. $\newline$ Answer:

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Identify independent and dependent events

Full solution

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 \mid B)

, rounding to the nearest thousandth, if necessary.

\newline

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. $\newline$ Since events $A$ and $B$ are independent, we can directly use the probability of $A$ for $P(A\mid B)$ . $\newline$ $P(A\mid B) = P(A) = 0.25$
Round Answer if Necessary: Round the answer to the nearest thousandth if necessary. $\newline$ 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. $\newline$ $P(A\mid B) = 0.25$

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