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In an experiment, the probability that event $A$ occurs is $\frac{2}{5}$ and the probability that event $B$ occurs is $\frac{3}{4}$ . If $A$ and $B$ are independent events, what is the probability that $A$ and $B$ both occur? $\newline$ Simplify any fractions. $\newline$

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Independence and conditional probability

Full solution

Q. In an experiment, the probability that event

A

occurs is

\frac{2}{5}

and the probability that event

B

occurs is

\frac{3}{4}

. If

A

and

B

are independent events, what is the probability that

A

and

B

both occur?

\newline

Simplify any fractions.

\newline

Multiply probabilities: Since $A$ and $B$ are independent, we multiply their probabilities to find the probability of both happening: $P(A \text{ and } B) = P(A) \times P(B)$ .
Calculate probability: $P(A) = \frac{2}{5}$ and $P(B) = \frac{3}{4}$ , so $P(A \text{ and } B) = \left(\frac{2}{5}\right) * \left(\frac{3}{4}\right)$ .
Perform multiplication: Now, let's do the multiplication: $(\frac{2}{5}) \times (\frac{3}{4}) = \frac{6}{20}$ .

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Question

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Question

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\newline

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\newline

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\newline

Write your answer as a decimal rounded to the nearest thousandth.

\newline

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\newline

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