Question

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

Explanation:

Step1: Calculate the probability of rolling a 5

A 6 - sided die has 6 possible outcomes. The probability of rolling a 5 is \(P(5)=\frac{1}{6}\)

Step2: Calculate the probability of rolling an odd number

The odd numbers on a 6 - sided die are 1, 3, 5. So there are 3 odd numbers. The probability of rolling an odd number is \(P(\text{odd})=\frac{3}{6}=\frac{1}{2}\)

Step3: Use the formula for independent events

Since the two rolls are independent events, the probability of both events occurring is \(P = P(5)\times P(\text{odd})\)
Substitute the values: \(P=\frac{1}{6}\times\frac{1}{2}\)

$$P=\frac{1\times1}{6\times2}=\frac{1}{12}$$

Answer:

\(\frac{1}{12}\)