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In an experiment, the probability that event $A$ occurs is $\frac{4}{7}$ , the probability that event $B$ occurs is $\frac{4}{7}$ , and the probability that events $A$ and $B$ both occur is $\frac{1}{3}$ . $\newline$ 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{4}{7}

, the probability that event

B

occurs is

\frac{4}{7}

, and the probability that events

A

and

B

both occur is

\frac{1}{3}

.

\newline

What is the probability that

A

occurs given that

B

occurs?

\newline

Simplify any fractions.

\newline

____

Use Conditional Probability Formula: To find the probability that $A$ occurs given that $B$ occurs, we use the formula for conditional probability: $P(A|B) = \frac{P(A \text{ and } B)}{P(B)}$ .
Calculate $P(A|B)$ : We know $P(A \text{ and } B) = \frac{1}{3}$ and $P(B) = \frac{4}{7}$ . So, $P(A|B) = \frac{\frac{1}{3}}{\frac{4}{7}}$ .
Multiply by Reciprocal: To divide the fractions, we multiply by the reciprocal of the second fraction: $(\frac{1}{3}) \times (\frac{7}{4})$ .
Multiply Numerators and Denominators: Now, multiply the numerators and denominators: $(1 \times 7) / (3 \times 4)$ .
Simplify to $\frac{7}{12}$ : This simplifies to $\frac{7}{12}$ . So, $P(A|B) = \frac{7}{12}$ .

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college students running for student government class president. The candidates include

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, the probability that event

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, and the probability that events

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B

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\newline

A

B

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\newline

\text{yes}

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\newline

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0.6

, the probability that a competitor was female is

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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.

\newline

If the server's claim is true, and one day he leaves candy with \(4\) customers' bills, what is the probability that exactly \(3\) of those customers will tip well?

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Question

There is a spinner with `50` equally likely sections, numbered from `1` to `50`. You have the opportunity to spin it. If the number is odd, you win $`11`. If the number is even, you win nothing. If you play the game, what is the expected payoff?\(\$\)_____

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Question

There are two different raffles you can enter.

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\newline

Which raffle is a better deal?

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\text{[A]Raffle A}

\newline

\text{[B]Raffle B}

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Question

X

is a normally distributed random variable with mean

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and standard deviation

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\newline

What is the probability that

X

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?

\newline

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rule and write your answer as a decimal. Round to the nearest thousandth if necessary.

\newline

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X

is a normally distributed random variable with mean

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and standard deviation

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\newline

What is the probability that

X

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68

?

\newline

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

\newline

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Question

Complete the statement. Round your answer to the nearest thousandth.

\newline

In a population that is normally distributed with mean

43

and standard deviation

3

30\%

of the values are those less than ______.

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