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In an experiment, the probability that event $A$ occurs is $\frac{7}{8}$ and the probability that event $B$ occurs is $\frac{3}{7}$ . 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{7}{8}

and the probability that event

B

occurs is

\frac{3}{7}

. If

A

and

B

are independent events, what is the probability that

A

and

B

both occur?

\newline

Simplify any fractions.

Calculate Probability of A and B: $P(A \text{ and } B) = P(A) \times P(B)$ cuz they're independent, right? So let's do the math: $P(A \text{ and } B) = \frac{7}{8} \times \frac{3}{7}.$
Multiply Numerators and Denominators: Now, we multiply the numerators together and the denominators together: $7 \times 3 = 21$ and $8 \times 7 = 56$ . So, $P(A \text{ and } B) = \frac{21}{56}$ .
Simplify Fraction: We gotta simplify the fraction $\frac{21}{56}$ . Both $21$ and $56$ can be divided by $7$ . So, $21 \div 7 = 3$ and $56 \div 7 = 8$ . The simplified fraction is $\frac{3}{8}$ .

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\newline

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\newline

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