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

Determine Probability of Rolling a 1: First, we need to determine the probability of rolling a 1 on a 6-sided die. Since there are 6 possible outcomes and only one of them is a 1, the probability of rolling a 1 is 1 out of 6. Calculation: P(rolling a 1) = 1/6Find Probability of Rolling a Number Less Than 2: Next, we need to determine the probability of rolling a number less than 2 on the second roll. The only number less than 2 on a 6-sided die is 1. Therefore, the probability of rolling a number less than 2 is the same as the probability of rolling a 1, which is 1 out of 6. Calculation: P(rolling a number less than 2) = 1/6Calculate Combined Probability: Now, we need to find the combined probability of both events happening in sequence. Since the two rolls are independent events, we multiply the probabilities of each event occurring. Calculation: P(rolling a 1 and then rolling a number less than 2) = P(rolling a 1) * P(rolling a number less than 2) = (1/6) * (1/6)Perform Final Multiplication: Performing the multiplication gives us the final probability. Calculation: (1/6) * (1/6) = 1/36

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

View step-by-step help

Home

Math Problems

Algebra 2

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

1

and then rolling a number less than

2

\newline

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

\newline

_____

Determine Probability of Rolling a $1$ : First, we need to determine the probability of rolling a $1$ on a $6$ -sided die. Since there are $6$ possible outcomes and only one of them is a $1$ , the probability of rolling a $1$ is $1$ out of $6$ . $\newline$ Calculation: $P(\text{rolling a } 1) = \frac{1}{6}$
Find Probability of Rolling a Number Less Than $2$ : Next, we need to determine the probability of rolling a number less than $2$ on the second roll. The only number less than $2$ on a $6$ -sided die is $1$ . Therefore, the probability of rolling a number less than $2$ is the same as the probability of rolling a $1$ , which is $1$ out of $6$ . $\newline$ Calculation: $P(\text{rolling a number less than } 2) = \frac{1}{6}$
Calculate Combined Probability: Now, we need to find the combined probability of both events happening in sequence. Since the two rolls are independent events, we multiply the probabilities of each event occurring. $\newline$ Calculation: $P(\text{rolling a } 1 \text{ and then rolling a number less than } 2) = P(\text{rolling a } 1) \times P(\text{rolling a number less than } 2) = \left(\frac{1}{6}\right) \times \left(\frac{1}{6}\right)$
Perform Final Multiplication: Performing the multiplication gives us the final probability. $\newline$ Calculation: $(\frac{1}{6}) \times (\frac{1}{6}) = \frac{1}{36}$