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In an experiment, the probability that event $A$ occurs is $\frac{2}{5}$ and the probability that event $B$ occurs is $\frac{3}{5}$ . 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{2}{5}

and the probability that event

B

occurs is

\frac{3}{5}

. If

A

and

B

are independent events, what is the probability that

A

and

B

both occur?

\newline

Simplify any fractions.

Multiply Fractions: Now, let's do the multiplication: $(\frac{2}{5}) \times (\frac{3}{5}) = \frac{6}{25}$ .
Final Result: No need to simplify further, $\frac{6}{25}$ is already in its simplest form.

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