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

Explanation:

Step1: Find prime - number probability

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

Step2: Find number - less - than - 4 probability

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

Step3: Use multiplication rule for independent events

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

Step4: Convert to percentage

To convert $\frac{1}{4}$ to a percentage, we calculate $\frac{1}{4}\times100% = 25%$.

Answer:

25%