You roll a 6-sided die two times. What is the probability of rolling an odd number and then rolling a 5? Simplify your answer and write it as a fraction or whole number. _____

Calculate Odd Probability: Determine the probability of rolling an odd number on a 6-sided die. There are 3 odd numbers on a 6-sided die (1, 3, and 5). The probability of rolling an odd number is the number of odd outcomes divided by the total number of outcomes. Calculation: P(odd) = 3/6 = 1/2Calculate 5 Probability: Determine the probability of rolling a 5 on a 6-sided die. There is only one outcome that is a 5 on a 6-sided die. The probability of rolling a 5 is the number of outcomes that are a 5 divided by the total number of outcomes. Calculation: P(5) = 1/6Calculate Joint Probability: Since the two dice rolls are independent events, the probability of both events occurring is the product of their individual probabilities. Calculation: P(odd then 5) = P(odd) * P(5) = (1/2) * (1/6) = 1/12

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You roll a $6$ -sided die two times. $\newline$ What is the probability of rolling an odd number and then rolling a $5$ ? $\newline$ 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 an odd number and then rolling a

5

\newline

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

\newline

_____

Calculate Odd Probability: Determine the probability of rolling an odd number on a $6$ -sided die. There are $3$ odd numbers on a $6$ -sided die ( $1$ , $3$ , and $5$ ). The probability of rolling an odd number is the number of odd outcomes divided by the total number of outcomes. Calculation: $P(\text{odd}) = \frac{3}{6} = \frac{1}{2}$
Calculate $5$ Probability: Determine the probability of rolling a $5$ on a $6$ -sided die. $\newline$ There is only one outcome that is a $5$ on a $6$ -sided die. $\newline$ The probability of rolling a $5$ is the number of outcomes that are a $5$ divided by the total number of outcomes. $\newline$ Calculation: $P(5) = \frac{1}{6}$
Calculate Joint Probability: Since the two dice rolls are independent events, the probability of both events occurring is the product of their individual probabilities. $\newline$ Calculation: $P(\text{odd then } 5) = P(\text{odd}) \times P(5) = \frac{1}{2} \times \frac{1}{6} = \frac{1}{12}$