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In an experiment, the probability that event $A$ occurs is $\frac{3}{7}$ and the probability that event $B$ occurs is $\frac{1}{8}$ . If $A$ and $B$ are independent events, what is the probability that $A$ and $B$ both occur? $\newline$ Simplify any fractions.

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Independence and conditional probability

Full solution

Q. In an experiment, the probability that event

A

occurs is

\frac{3}{7}

and the probability that event

B

occurs is

\frac{1}{8}

. If

A

and

B

are independent events, what is the probability that

A

and

B

both occur?

\newline

Simplify any fractions.

Calculate $P(A \text{ and } B)$ : $P(A) = \frac{3}{7}$ and $P(B) = \frac{1}{8}$ . Since $A$ and $B$ are independent, $P(A \text{ and } B) = P(A) \times P(B)$ .
Multiply $P(A)$ and $P(B)$ : Now calculate $P(A \text{ and } B) = \frac{3}{7} \times \frac{1}{8}$ .
Final Probability Calculation: $P(A \text{ and } B) = \frac{3}{7} \times \frac{1}{8} = \frac{3}{56}$ .

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