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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 $4$ ? $\newline$ 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

4

?

\newline

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

\newline

_____

Determine probability of first roll: Determine the probability of rolling a number less than $2$ on the first roll. $\newline$ Since a $6$ -sided die has only one number less than $2$ (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 of second roll: Determine the probability of rolling a $4$ on the second roll. $\newline$ Since a $6$ -sided die has one $4$ , the probability of rolling a $4$ is also $1$ out of $6$ . $\newline$ Calculation: $P(\text{rolling a } 4) = \frac{1}{6}$
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: $P(\text{rolling a number less than 2 and then a 4}) = P(\text{rolling a number less than 2}) \times P(\text{rolling a 4}) = \frac{1}{6} \times \frac{1}{6}$
Calculate final probability: Calculate the product of the two probabilities. $\newline$ Calculation: $(\frac{1}{6}) \times (\frac{1}{6}) = \frac{1}{36}$

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\newline

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\newline

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Which raffle is a better deal?

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\newline

\text{[B]Raffle B}

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Question

X

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\newline

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\newline

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\newline

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

\newline

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