Question

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

Explanation:

Step1: Determine the probability of rolling a prime number

A 6 - sided die has numbers \(1,2,3,4,5,6\). Prime numbers among them are \(2\), \(3\), \(5\). So there are \(3\) prime numbers. The probability of rolling a prime number \(P(\text{prime})=\frac{3}{6}=\frac{1}{2}\)

Step2: Determine the probability of rolling a 6

The probability of rolling a 6 on a 6 - sided die \(P(6)=\frac{1}{6}\)

Step3: Use the multiplication rule for independent events

Since the two rolls are independent events, the probability of rolling a prime number and then rolling a 6 is \(P = P(\text{prime})\times P(6)\)
Substitute the values: \(P=\frac{1}{2}\times\frac{1}{6}\)

$$P=\frac{1\times1}{2\times6}=\frac{1}{12}$$

Answer:

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