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You roll a $6$ -sided die two times. $\newline$ What is the probability of rolling a number less than $2$ and then rolling a $1$ ? $\newline$ Simplify your answer and write it as a fraction or whole number. $\newline$ _____

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Probability of independent and dependent events

Full solution

Q. You roll a

6

-sided die two times.

\newline

What is the probability of rolling a number less than

2

and then rolling a

1

?

\newline

Simplify your answer and write it as a fraction or whole number.

\newline

_____

Determine probability first roll: Determine the probability of rolling a number less than $2$ on the first roll. $\newline$ Since there is only one number less than $2$ on a $6$ -sided die (which is $1$ ), the probability of rolling a number less than $2$ is $1$ out of $6$ . $\newline$ Calculation: $P(\text{rolling a number less than } 2) = \frac{1}{6}$
Determine probability second roll: Determine the probability of rolling a $1$ on the second roll. $\newline$ The probability of rolling a $1$ on a $6$ -sided die is also $1$ out of $6$ , since there is only one outcome that is a $1$ among the six possible outcomes. $\newline$ Calculation: $P(\text{rolling a } 1) = \frac{1}{6}$
Calculate combined probability: Since the two rolls are independent events, the probability of both events occurring is the product of their individual probabilities. $\newline$ Calculation: $P(\text{rolling a number less than } 2 \text{ and then rolling a } 1) = P(\text{rolling a number less than } 2) \times P(\text{rolling a } 1) = \frac{1}{6} \times \frac{1}{6}$
Perform multiplication: Perform the multiplication to find the combined probability. $\newline$ Calculation: $(\frac{1}{6}) \times (\frac{1}{6}) = \frac{1}{36}$

More problems from Probability of independent and dependent events

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

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In an experiment, the probability that event

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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

\newline

\text{yes}

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Question

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\newline

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0.6

, the probability that a competitor was female is

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

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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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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 are two different raffles you can enter.

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

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

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\newline

Which raffle is a better deal?

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\newline

\text{[A]Raffle A}

\newline

\text{[B]Raffle B}

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Question

X

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and standard deviation

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\newline

What is the probability that

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?

\newline

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\newline

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X

is a normally distributed random variable with mean

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\newline

What is the probability that

X

62

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

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30\%

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