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

Calculate Probability of Rolling 5: Since a standard 6-sided die has numbers 1 through 6, the probability of rolling a 5 on the first roll is 1 out of 6 possible outcomes. Calculation: P(rolling a 5) = 1/6Calculate Probability of Rolling Number Greater Than 5: For the second roll, the only number greater than 5 on a 6-sided die is 6. Therefore, the probability of rolling a number greater than 5 is also 1 out of 6 possible outcomes. Calculation: P(rolling a number greater than 5) = 1/6Find Probability of Both Events in Sequence: To find the probability of both events happening in sequence (rolling a 5 first and then a number greater than 5), we multiply the probabilities of the individual events because they are independent. Calculation: P(rolling a 5 and then a number greater than 5) = P(rolling a 5) * P(rolling a number greater than 5) = (1/6) * (1/6)Perform Multiplication for Final Probability: Performing the multiplication gives us the probability of the sequence of rolls. 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 $5$ and then rolling a number greater than $5$ ? $\newline$ 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 a

5

and then rolling a number greater than

5

\newline

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

\newline

_____

Calculate Probability of Rolling $5$ : Since a standard $6$ -sided die has numbers $1$ through $6$ , the probability of rolling a $5$ on the first roll is $1$ out of $6$ possible outcomes. $\newline$ Calculation: $P(\text{rolling a } 5) = \frac{1}{6}$
Calculate Probability of Rolling Number Greater Than $5$ : For the second roll, the only number greater than $5$ on a $6$ -sided die is $6$ . Therefore, the probability of rolling a number greater than $5$ is also $1$ out of $6$ possible outcomes. $\newline$ Calculation: $P(\text{rolling a number greater than } 5) = \frac{1}{6}$
Find Probability of Both Events in Sequence: To find the probability of both events happening in sequence (rolling a $5$ first and then a number greater than $5$ ), we multiply the probabilities of the individual events because they are independent. $\newline$ Calculation: $P(\text{rolling a 5 and then a number greater than 5}) = P(\text{rolling a 5}) \times P(\text{rolling a number greater than 5}) = \frac{1}{6} \times \frac{1}{6}$
Perform Multiplication for Final Probability: Performing the multiplication gives us the probability of the sequence of rolls. $\newline$ Calculation: $(\frac{1}{6}) \times (\frac{1}{6}) = \frac{1}{36}$