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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 $\frac{4}{7}$ . 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{3}{7}

and the probability that event

B

occurs is

\frac{4}{7}

. If

A

and

B

are independent events, what is the probability that

A

and

B

both occur?

\newline

Simplify any fractions.

Multiply numerators: Now, let's do the math. Multiplying the numerators, we get $3 \times 4 = 12$ . Multiplying the denominators, we get $7 \times 7 = 49$ . So, the probability that both A and B occur is $\frac{12}{49}$ .

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