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

Explanation:

Step1: Find probability of first - roll

A 6 - sided die has 6 possible outcomes. Numbers greater than 3 are 4, 5, 6. So there are 3 favorable outcomes. The probability of rolling a number greater than 3 on the first roll, $P_1=\frac{3}{6}=\frac{1}{2}$.

Step2: Find probability of second - roll

Numbers less than 4 are 1, 2, 3. So there are 3 favorable outcomes. The probability of rolling a number less than 4 on the second roll, $P_2=\frac{3}{6}=\frac{1}{2}$.

Step3: Use multiplication rule for independent events

Since the two rolls of the die are independent events, the probability of both events occurring is $P = P_1\times P_2$. Substituting the values of $P_1$ and $P_2$, we get $P=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Step4: Convert to percentage

To convert $\frac{1}{4}$ to a percentage, we multiply by 100. So $P=\frac{1}{4}\times100 = 25%$.

Answer:

25%