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In an experiment, the probability that event $A$ occurs is $\frac{1}{5}$ 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}{5}

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: $P(A \text{ and } B) = P(A) \times P(B)$ cuz they're independent, so let's multiply the probabilities.
Calculate Individual Probabilities: $P(A \text{ and } B) = \frac{1}{5} \times \frac{1}{7}$ . Just gotta multiply the tops and bottoms.
Multiply Probabilities: $P(A \text{ and } B) = \frac{1 \times 1}{5 \times 7}$ . That's $\frac{1}{35}$ , right?
Final Probability: No need to simplify, $\frac{1}{35}$ is as simple as it gets.

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\newline

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\newline

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\newline

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