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Given that events A and B are independent with
P(A)=0.95 and
P(B)=0.4, determine the value of
P(A∣B), rounding to the nearest thousandth, if necessary.
Answer:

Given that events A and B are independent with $P(A)=0.95$ and $P(B)=0.4$ , determine the value of $P(A \mid B)$ , rounding to the nearest thousandth, if necessary. $\newline$ Answer:

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Identify independent events

Full solution

Q. Given that events A and B are independent with

P(A)=0.95

and

P(B)=0.4

, determine the value of

P(A \mid B)

, rounding to the nearest thousandth, if necessary.

\newline

Answer:

Probability of Independent Events: For independent events $A$ and $B$ , the probability of $A$ given $B$ , denoted as $P(A\mid B)$ , is the same as the probability of $A$ , because the occurrence of $B$ does not affect the probability of $A$ . Therefore, $P(A\mid B) = P(A)$ .
Calculation of P(A): We are given $P(A) = 0.95$ . Since $A$ and $B$ are independent, $P(A\mid B) = P(A)$ .
Final Value of $P(A|B)$ : Now we can directly write the value of $P(A∣B)$ as $0.95$ .

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