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

Explanation:

Step1: Calculate first - roll probability

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

Step2: Calculate second - roll probability

Numbers less than 4 on a 6 - sided die are 1, 2, 3. So the probability of rolling a number less than 4 in the second roll is $P_2=\frac{3}{6}=\frac{1}{2}$.

Step3: Calculate combined probability

Since the two rolls are independent events, the probability of both events occurring is the product of their individual probabilities. So $P = P_1\times P_2=\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

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%