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In an experiment, the probability that event $A$ occurs is $\frac{4}{5}$ and the probability that event $B$ occurs is $\frac{4}{5}$ . 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{4}{5}

and the probability that event

B

occurs is

\frac{4}{5}

. If

A

and

B

are independent events, what is the probability that

A

and

B

both occur?

\newline

Simplify any fractions.

Given Probabilities: $P(A)$ is given as $\frac{4}{5}$ and $P(B)$ is also given as $\frac{4}{5}$ . So, we calculate $P(A \text{ and } B) = \frac{4}{5} \times \frac{4}{5}$ .
Calculate $P(A \text{ and } B)$ : Performing the multiplication, we get $P(A \text{ and } B) = \frac{16}{25}$ .

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