Question

you roll a 6 - sided die two times. what is the probability of rolling an even number and then rolling a number greater than 4? write your answer as a percentage rounded to the nearest tenth.

Explanation:

Step1: Calculate probability of rolling an even number

The even numbers on a 6 - sided die are 2, 4, 6. So there are 3 even numbers out of 6 possible outcomes. The probability of rolling an even number $P(E)=\frac{3}{6}=\frac{1}{2}$.

Step2: Calculate probability of rolling a number greater than 4

The numbers greater than 4 on a 6 - sided die are 5, 6. So there are 2 numbers out of 6 possible outcomes. The probability of rolling a number greater than 4 $P(G)=\frac{2}{6}=\frac{1}{3}$.

Step3: Use the multiplication rule for independent events

Since the two die - rolls are independent events, the probability of both events occurring is the product of their individual probabilities. $P = P(E)\times P(G)=\frac{1}{2}\times\frac{1}{3}=\frac{1}{6}$.

Step4: Convert to percentage

To convert $\frac{1}{6}$ to a percentage, we calculate $\frac{1}{6}\times100\approx16.7\%$.

Answer:

$16.7\%$