You roll a 6-sided die two times. What is the probability of rolling a 5 and then rolling a number less than 4? Simplify your answer and write it as a fraction or whole number. _____

Calculate Probability of Rolling a 5: Determine the probability of rolling a 5 on the first roll. Since there are 6 possible outcomes on a 6-sided die, and only one of those outcomes is a 5, the probability of rolling a 5 is 1 out of 6. Calculation: P(rolling a 5) = 1/6Calculate Probability of Rolling a Number Less Than 4: Determine the probability of rolling a number less than 4 on the second roll. The numbers less than 4 on a 6-sided die are 1, 2, and 3. There are 3 favorable outcomes out of 6 possible outcomes. Calculation: P(rolling a number less than 4) = 3/6 = 1/2Calculate 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 5 and then rolling a number less than 4) = P(rolling a 5) * P(rolling a number less than 4) = (1/6) * (1/2)Perform Multiplication: Perform the multiplication to find the combined probability. Calculation: (1/6) * (1/2) = 1/12

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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 less than $4$ ? $\newline$ 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

5

and then rolling a number less than

4

\newline

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

\newline

_____

Calculate Probability of Rolling a $5$ : Determine the probability of rolling a $5$ on the first roll. Since there are $6$ possible outcomes on a $6$ -sided die, and only one of those outcomes is a $5$ , the probability of rolling a $5$ is $1$ out of $6$ . Calculation: $P(\text{rolling a } 5) = \frac{1}{6}$
Calculate Probability of Rolling a Number Less Than $4$ : Determine the probability of rolling a number less than $4$ on the second roll. $\newline$ The numbers less than $4$ on a $6$ -sided die are $1$ , $2$ , and $3$ . There are $3$ favorable outcomes out of $6$ possible outcomes. $\newline$ Calculation: $P(\text{rolling a number less than 4}) = \frac{3}{6} = \frac{1}{2}$
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: $P(\text{rolling a } 5 \text{ and then rolling a number less than } 4) = P(\text{rolling a } 5) \times P(\text{rolling a number less than } 4) = \frac{1}{6} \times \frac{1}{2}$
Perform Multiplication: Perform the multiplication to find the combined probability. $\newline$ Calculation: $(\frac{1}{6}) \times (\frac{1}{2}) = \frac{1}{12}$