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In an experiment, the probability that event $A$ occurs is $\frac{1}{9}$ and the probability that event $B$ occurs is $\frac{1}{3}$ . 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{1}{9}

and the probability that event

B

occurs is

\frac{1}{3}

. If

A

and

B

are independent events, what is the probability that

A

and

B

both occur?

\newline

Simplify any fractions.

\newline

Use Independence Rule: $P(A \text{ and } B) = P(A) \times P(B)$ since $A$ and $B$ are independent.
Calculate Individual Probabilities: $P(A) = \frac{1}{9}$ and $P(B) = \frac{1}{3}$ .
Calculate Joint Probability: $P(A \text{ and } B) = \frac{1}{9} \times \frac{1}{3}$ .
Final Probability Calculation: $P(A \text{ and } B) = \frac{1}{27}$ .

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Question

In an experiment, the probability that event

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, the probability that event

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, and the probability that events

A

B

\frac{1}{9}

\newline

A

B

independent events?

\newline

\newline

\text{yes}

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Question

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\newline

The probability that a competitor reacted in over

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0.6

, the probability that a competitor was female is

0.4

, and the probability that a competitor reacted in over

0.7

seconds and was female is

0.3

\newline

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Write your answer as a whole number, decimal, or simplified fraction.

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Question

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\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

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Question

There are two different raffles you can enter.

\newline

In raffle A, one ticket will win a `$720` prize, and the other tickets will win nothing. There are

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\newline

Raffle B is for a `$370` prize. Out of

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\newline

Which raffle is a better deal?

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Question

X

is a normally distributed random variable with mean

49

and standard deviation

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\newline

What is the probability that

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74

?

\newline

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\newline

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Question

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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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