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In an experiment, the probability that event $A$ occurs is $\frac{7}{8}$ , the probability that event $B$ occurs is $\frac{1}{2}$ , and the probability that events $A$ and $B$ both occur is $\frac{3}{7}$ . $\newline$ What is the probability that $A$ occurs given that $B$ occurs? $\newline$ Simplify any fractions. $\newline$ ____

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Find conditional probabilities

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Q. In an experiment, the probability that event

A

occurs is

\frac{7}{8}

, the probability that event

B

occurs is

\frac{1}{2}

, and the probability that events

A

and

B

both occur is

\frac{3}{7}

.

\newline

What is the probability that

A

occurs given that

B

occurs?

\newline

Simplify any fractions.

\newline

____

Use Formula: To find the probability that A occurs given that B occurs, we use the formula $P(A|B) = \frac{P(A \text{ and } B)}{P(B)}$ .
Calculate $P(A \text{ and } B)$ : We know $P(A \text{ and } B) = \frac{3}{7}$ and $P(B) = \frac{1}{2}$ .
Calculate $P(A|B)$ : Now we calculate $P(A|B) = \frac{3}{7} / \frac{1}{2}$ .
Multiply Fractions: To divide by a fraction, we multiply by its reciprocal. So, $P(A|B) = \frac{3}{7} \times \frac{2}{1}$ .
Final Probability Calculation: Multiplying the fractions, we get $P(A|B) = \frac{3 \times 2}{7 \times 1} = \frac{6}{7}$ .

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\newline

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\newline

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\newline

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\newline

Write your answer as a decimal rounded to the nearest thousandth.

\newline

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\newline

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