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In an experiment, the probability that event $A$ occurs is $\frac{1}{3}$ and the probability that event $B$ occurs is $\frac{1}{7}$ . 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{1}{3}

and the probability that event

B

occurs is

\frac{1}{7}

. If

A

and

B

are independent events, what is the probability that

A

and

B

both occur?

\newline

Simplify any fractions.

Identify Independence: Since $A$ and $B$ are independent, the probability of both happening is $P(A) \times P(B)$ . So we gotta multiply $\frac{1}{3}$ by $\frac{1}{7}$ .
Calculate Probability: Multiplying the probabilities gives us $\frac{1}{3} \times \frac{1}{7} = \frac{1}{21}$ . That's our answer, no need to simplify, it's already in its simplest form.

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