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In an experiment, the probability that event $A$ occurs is $\frac{5}{7}$ 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{5}{7}

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.

Identify Probabilities: So, $A$ 's $\frac{5}{7}$ and $B$ 's $\frac{4}{5}$ . Since they're independent, just multiply 'em to find the chance they both happen. So it's like $\frac{5}{7} \times \frac{4}{5}$ .
Calculate Multiplication: Now, do the math. Multiply the tops (numerators) and then the bottoms (denominators). That's $5 \times 4$ for the top and $7 \times 5$ for the bottom. So, $\frac{20}{35}.$

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