Given that events A and B are independent with P(A)=0.09 and P(B)=0.3, determine the value of P(B∣A), rounding to the nearest thousandth, if necessary. Answer:

Understand concept of conditional probability: Understand the concept of conditional probability for independent events. For independent events A and B, the probability of B given A, denoted as P(B∣A), is the same as the probability of B, because the occurrence of A does not affect the probability of B.Apply concept to given probabilities: Apply the concept to the given probabilities. Since A and B are independent, P(B∣A) = P(B). Given P(B) = 0.3, we can directly state that P(B∣A) = 0.3.Round answer if necessary: Round the answer to the nearest thousandth if necessary. P(B∣A) = 0.3 does not require rounding to the nearest thousandth, as it is already at that precision level.

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Given that events A and B are independent with
P(A)=0.09 and
P(B)=0.3, determine the value of
P(B∣A), rounding to the nearest thousandth, if necessary.
Answer:

Given that events A and B are independent with $P(A)=0.09$ and $P(B)=0.3$ , determine the value of $P(B \mid A)$ , rounding to the nearest thousandth, if necessary. $\newline$ Answer:

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Q. Given that events A and B are independent with

P(A)=0.09

and

P(B)=0.3

, determine the value of

P(B \mid A)

, rounding to the nearest thousandth, if necessary.

\newline

Answer:

Understand concept of conditional probability: Understand the concept of conditional probability for independent events. For independent events $A$ and $B$ , the probability of $B$ given $A$ , denoted as $P(B\mid A)$ , is the same as the probability of $B$ , because the occurrence of $A$ does not affect the probability of $B$ .
Apply concept to given probabilities: Apply the concept to the given probabilities. $\newline$ Since $A$ and $B$ are independent, $P(B\mid A) = P(B)$ . $\newline$ Given $P(B) = 0.3$ , we can directly state that $P(B\mid A) = 0.3$ .
Round answer if necessary: Round the answer to the nearest thousandth if necessary. $P(B\mid A) = 0.3$ does not require rounding to the nearest thousandth, as it is already at that precision level.