Question

you roll a 6 - sided die two times. what is the probability of rolling a 3 and then rolling a prime number? simplify your answer and write it as a fraction or whole number.

Explanation:

Step1: Calculate the probability of rolling a 3

The probability of rolling a 3 on a 6 - sided die is \(P(3)=\frac{1}{6}\) since there is 1 favorable outcome (rolling a 3) out of 6 possible outcomes (\(1,2,3,4,5,6\)).

Step2: Calculate the probability of rolling a prime number

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

Step3: Use the multiplication rule for independent events

Since the two rolls of the die are independent events (the outcome of the first roll does not affect the outcome of the second roll), we use the formula \(P(A\cap B)=P(A)\times P(B)\)
Here, \(A\) is the event of rolling a 3 and \(B\) is the event of rolling a prime number. So \(P = \frac{1}{6}\times\frac{1}{2}\)

Answer:

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