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

Calculate Probability of Rolling a 1: Determine the probability of rolling a 1 on the first roll. Since there are 6 sides on a die, each with an equal chance of landing face up, the probability of rolling a 1 on the first roll is 1 out of 6. Calculation: P(rolling a 1) = 1/6Calculate Probability of Rolling Greater Number: Determine the probability of rolling a number greater than 1 on the second roll. There are 5 numbers greater than 1 on a 6-sided die (2, 3, 4, 5, and 6). Therefore, the probability of rolling a number greater than 1 on the second roll is 5 out of 6. Calculation: P(rolling a number greater than 1) = 5/6Calculate 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 1 and then a number greater than 1) = P(rolling a 1) * P(rolling a number greater than 1) = (1/6) * (5/6)Perform Multiplication: Perform the multiplication to find the combined probability. Calculation: (1/6) * (5/6) = 5/36

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You roll a $6$ -sided die two times. $\newline$ What is the probability of rolling a $1$ and then rolling a number greater than $1$ ? $\newline$ 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

1

and then rolling a number greater than

1

\newline

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

\newline

_____

Calculate Probability of Rolling a $1$ : Determine the probability of rolling a $1$ on the first roll. Since there are $6$ sides on a die, each with an equal chance of landing face up, the probability of rolling a $1$ on the first roll is $1$ out of $6$ . Calculation: $P(\text{rolling a } 1) = \frac{1}{6}$
Calculate Probability of Rolling Greater Number: Determine the probability of rolling a number greater than $1$ on the second roll. $\newline$ There are $5$ numbers greater than $1$ on a $6$ -sided die ( $2$ , $3$ , $4$ , $5$ , and $6$ ). Therefore, the probability of rolling a number greater than $1$ on the second roll is $5$ out of $6$ . $\newline$ Calculation: $5$ $2$
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: $P(\text{rolling a } 1 \text{ and then a number greater than } 1) = P(\text{rolling a } 1) \times P(\text{rolling a number greater than } 1) = \frac{1}{6} \times \frac{5}{6}$
Perform Multiplication: Perform the multiplication to find the combined probability. $\newline$ Calculation: $(\frac{1}{6}) \times (\frac{5}{6}) = \frac{5}{36}$