you roll a 6 - sided die two times. what is the probability of rolling a number greater than 3 and then…

Explanation:

Step1: Calculate single - roll probability

The numbers greater than 3 on a 6 - sided die are 4, 5, 6. So the probability of rolling a number greater than 3 in a single roll is $P_1=\frac{3}{6}=\frac{1}{2}$.

Step2: Use multiplication rule for independent events

Since the two die - rolls are independent events, the probability of rolling a number greater than 3 on the first roll and then rolling a number greater than 3 on the second roll is $P = P_1\times P_1$. Substituting $P_1=\frac{1}{2}$, we get $P=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Step3: Convert to percentage

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

Answer:

25%