Given P(A)=0.3,P(B)=0.7 and P(A and B)=0.26, find the value of P(B∣A), rounding to the nearest thousandth, if necessary. Answer:

Understand definition of conditional probability: Understand the definition of conditional probability. The conditional probability of B given A, denoted as P(B∣A), is defined as the probability that event B occurs given that event A has already occurred. The formula for conditional probability is: P(B∣A) = P(A and B) / P(A)Plug in given values: Plug in the given values into the conditional probability formula. We are given P(A) = 0.3, P(B) = 0.7, and P(A and B) = 0.26. Using these values, we can calculate P(B∣A) as follows: P(B∣A) = P(A and B) / P(A) P(B∣A) = 0.26 / 0.3Perform division: Perform the division to find P(B∣A). P(B∣A) = 0.26 / 0.3 P(B∣A) ≈ 0.866666...Round the result: Round the result to the nearest thousandth. P(B∣A) ≈ 0.867

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Given
P(A)=0.3,P(B)=0.7 and
P(A and
B)=0.26, find the value of
P(B∣A), rounding to the nearest thousandth, if necessary.
Answer:

Given $P(A)=0.3, P(B)=0.7$ and $P(A$ and $B)=0.26$ , find the value of $P(B \mid A)$ , rounding to the nearest thousandth, if necessary. $\newline$ Answer:

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Q. Given

P(A)=0.3, P(B)=0.7

and

P(A

and

B)=0.26

, find the value of

P(B \mid A)

, rounding to the nearest thousandth, if necessary.

\newline

Answer:

Understand definition of conditional probability: Understand the definition of conditional probability. $\newline$ The conditional probability of B given A, denoted as $P(B\mid A)$ , is defined as the probability that event B occurs given that event A has already occurred. The formula for conditional probability is: $\newline$ $P(B\mid A) = \frac{P(A \text{ and } B)}{P(A)}$
Plug in given values: Plug in the given values into the conditional probability formula. $\newline$ We are given $P(A) = 0.3$ , $P(B) = 0.7$ , and $P(A \text{ and } B) = 0.26$ . Using these values, we can calculate $P(B\mid A)$ as follows: $\newline$ $P(B\mid A) = \frac{P(A \text{ and } B)}{P(A)}$ $\newline$ $P(B\mid A) = \frac{0.26}{0.3}$
Perform division: Perform the division to find $P(B\mid A)$ . $P(B\mid A) = \frac{0.26}{0.3}$ $P(B\mid A) \approx 0.866666...$
Round the result: Round the result to the nearest thousandth. $P(B\mid A) \approx 0.867$