Question

you roll a 6 - sided die two times. what is the probability of rolling a number less than 4 and then rolling a number less than 4? write your answer as a percentage.

Explanation:

Step1: Calculate first - roll probability

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

Step2: Calculate second - roll probability

Since the rolls are independent events, the probability of rolling a number less than 4 on the second roll is also $\frac{3}{6}=\frac{1}{2}$.

Step3: Calculate combined probability

For independent events A and B, the probability of both A and B occurring is $P(A)\times P(B)$. So the probability of rolling a number less than 4 on the first roll and then rolling a number less than 4 on the second roll is $\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Step4: Convert to percentage

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

Answer:

25%