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

Explanation:

Step1: Identify prime numbers on a 6 - sided die

The prime numbers on a 6 - sided die (1, 2, 3, 4, 5, 6) are 2, 3, 5. So there are 3 prime numbers out of 6 possible outcomes.

Step2: Calculate the probability of rolling a prime number on the first roll

The probability of an event is the number of favorable outcomes divided by the number of total outcomes. For the first roll, the probability $P_1$ of rolling a prime number is $P_1=\frac{3}{6}=\frac{1}{2}$.

Step3: Calculate the probability of rolling a prime number on the second roll

Since the rolls are independent events, the probability $P_2$ of rolling a prime number on the second roll is also $P_2 = \frac{3}{6}=\frac{1}{2}$.

Step4: Calculate the probability of both events occurring

For independent events $A$ and $B$, the probability of both $A$ and $B$ occurring is $P(A\cap B)=P(A)\times P(B)$. So the probability $P$ of rolling a prime number and then rolling a prime number is $P=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Step5: Convert the fraction to a percentage

To convert $\frac{1}{4}$ to a percentage, we use the formula $\text{Percentage}= \frac{1}{4}\times100% = 25%$.

Answer:

25%