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

Explanation:

Step1: Calculate first - roll probability

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

Step2: Calculate second - 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 on the second roll is $P_2=\frac{3}{6}=\frac{1}{2}$.

Step3: Use multiplication rule for independent events

Since the two die - rolls are independent events, the probability of both events occurring is $P = P_1\times P_2$. Substitute $P_1=\frac{5}{6}$ and $P_2=\frac{1}{2}$ into the formula: $P=\frac{5}{6}\times\frac{1}{2}=\frac{5}{12}$.

Answer:

$\frac{5}{12}$