You roll a 6-sided die two times. What is the probability of rolling a number less than 2 and then rolling a 4? Simplify your answer and write it as a fraction or whole number. _____

Determine probability of first roll: Determine the probability of rolling a number less than 2 on the first roll. 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. Calculation: P(rolling a number less than 2) = 1/6Determine probability of second roll: Determine the probability of rolling a 4 on the second roll. Since a 6-sided die has one 4, the probability of rolling a 4 is also 1 out of 6. Calculation: P(rolling a 4) = 1/6Calculate combined probability: Since the two rolls are independent events, the probability of both events occurring is the product of their individual probabilities. Calculation: P(rolling a number less than 2 and then a 4) = P(rolling a number less than 2) * P(rolling a 4) = (1/6) * (1/6)Calculate final probability: Calculate the product of the two probabilities. Calculation: (1/6) * (1/6) = 1/36

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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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Math Problems

Algebra 2

Probability of independent and dependent events

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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: $(\frac{1}{6}) \times (\frac{1}{6}) = \frac{1}{36}$