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In an experiment, the probability that event $A$ occurs is $\frac{5}{6}$ and the probability that event $B$ occurs is $\frac{2}{9}$ . 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{5}{6}

and the probability that event

B

occurs is

\frac{2}{9}

. If

A

and

B

are independent events, what is the probability that

A

and

B

both occur?

\newline

Simplify any fractions.

Multiply Probabilities: To find the probability of both $A$ and $B$ happening, we multiply their probabilities together since they're independent. So, we do $\frac{5}{6} \times \frac{2}{9}.$
Calculate Result: Calculating that out, we get $(5\times2)/(6\times9)$ , which is $10/54$ .
Simplify Fraction: Now we gotta simplify $\frac{10}{54}$ . Both $10$ and $54$ are divisible by $2$ , so if we divide them by $2$ , we get $\frac{5}{27}$ .

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