you roll a 6 - sided die two times. what is the probability of rolling a prime number and then rolling a…

Explanation:

Step1: Find probability of rolling a prime number

The prime - numbered outcomes on a 6 - sided die are 2, 3, 5. So there are 3 prime - numbered outcomes out of 6 possible outcomes. The probability of rolling a prime number, $P(A)=\frac{3}{6}=\frac{1}{2}$.

Step2: Find probability of rolling a number greater than 3

The numbers greater than 3 on a 6 - sided die are 4, 5, 6. So there are 3 numbers greater than 3 out of 6 possible outcomes. The probability of rolling a number greater than 3, $P(B)=\frac{3}{6}=\frac{1}{2}$.

Step3: Use the multiplication rule for independent events

Since the two rolls of the die are independent events, the probability of both events occurring is the product of their individual probabilities. $P(A\cap B)=P(A)\times P(B)$. Substitute $P(A)=\frac{1}{2}$ and $P(B)=\frac{1}{2}$ into the formula. $P(A\cap B)=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}=0.25$.

Answer:

0.25