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

Explanation:

Step1: Identify prime - numbers on a 6 - sided die

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

Step2: Use the multiplication rule for independent events

Since the two rolls of the die are independent events, the probability of rolling a prime number on the first roll and then rolling a prime number on the second roll is $P(A)\times P(A)$. Substitute $P(A)=\frac{1}{2}$ into the formula: $\frac{1}{2}\times\frac{1}{2}=\frac{1}{4}$.

Step3: Convert to decimal

$\frac{1}{4}=0.25$

Answer:

0.25