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In an experiment, the probability that event $A$ occurs is $\frac{5}{6}$ , the probability that event $B$ occurs is $\frac{4}{5}$ , and the probability that events $A$ and $B$ both occur is $\frac{2}{3}$ . $\newline$ What is the probability that $A$ occurs given that $B$ occurs? $\newline$ Simplify any fractions. $\newline$ ____

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Find conditional probabilities

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Q. In an experiment, the probability that event

A

occurs is

\frac{5}{6}

, the probability that event

B

occurs is

\frac{4}{5}

, and the probability that events

A

and

B

both occur is

\frac{2}{3}

.

\newline

What is the probability that

A

occurs given that

B

occurs?

\newline

Simplify any fractions.

\newline

____

Use Formula: To find the probability that A occurs given that B occurs, we use the formula $P(A|B) = \frac{P(A \text{ and } B)}{P(B)}$ .
Calculate Probabilities: We know $P(A \text{ and } B) = \frac{2}{3}$ and $P(B) = \frac{4}{5}$ .
Divide Fractions: Now we calculate $P(A|B) = \frac{2}{3} / \frac{4}{5}.$
Multiply Numerators: To divide the fractions, we multiply by the reciprocal of the second fraction: $(\frac{2}{3}) \times (\frac{5}{4})$ .
Simplify Fraction: Multiplying the numerators and denominators, we get $(2 \times 5) / (3 \times 4) = 10/12$ .
Simplify Fraction: Multiplying the numerators and denominators, we get $(2 \times 5) / (3 \times 4) = 10/12$ .We can simplify $10/12$ by dividing both numerator and denominator by $2$ , which gives us $5/6$ .

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\newline

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Question

A restaurant server claims that \(28\)% of the time he leaves candy with the bill, the customer tips well.

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Which raffle is a better deal?

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\text{[B]Raffle B}

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Question

X

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\newline

What is the probability that

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\newline

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\newline

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is a normally distributed random variable with mean

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\newline

What is the probability that

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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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30\%

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