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In an experiment, the probability that event $A$ occurs is $\frac{3}{4}$ and the probability that event $B$ occurs is $\frac{7}{9}$ . 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}{4}

and the probability that event

B

occurs is

\frac{7}{9}

. If

A

and

B

are independent events, what is the probability that

A

and

B

both occur?

\newline

Simplify any fractions.

Multiply Probabilities: Since $A$ and $B$ are independent, multiply the probabilities: $P(A \text{ and } B) = P(A) \times P(B) = \frac{3}{4} \times \frac{7}{9}$ .
Do the Multiplication: Do the multiplication: $\frac{3}{4} \times \frac{7}{9} = \frac{21}{36}.$

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