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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 $\frac{7}{8}$ . 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{7}{8}

. If

A

and

B

are independent events, what is the probability that

A

and

B

both occur?

\newline

Simplify any fractions.

\newline

Calculate Probabilities: $P(A)$ is $\frac{2}{5}$ and $P(B)$ is $\frac{7}{8}$ . Since $A$ and $B$ are independent, $P(A \text{ and } B) = P(A) \times P(B)$ .
Multiply Probabilities: Now, let's multiply the probabilities: $P(A \text{ and } B) = \left(\frac{2}{5}\right) \times \left(\frac{7}{8}\right)$ .
Perform Multiplication: Do the multiplication: $\frac{2}{5} \times \frac{7}{8} = \frac{14}{40}$ .

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B

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\text{yes}

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0.6

, the probability that a competitor was female is

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Question

There are two different raffles you can enter.

\newline

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\newline

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Question

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\newline

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\newline

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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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