ralph rolls a single die two times in a row. what is the probability that he will roll a \three\ both times…

Explanation:

Step1: Probability of rolling a 3 on first roll

The probability of rolling a 3 on a single - die roll is $\frac{1}{6}$ since there is 1 favorable outcome (rolling a 3) out of 6 possible outcomes (1, 2, 3, 4, 5, 6).

Step2: Probability of rolling a 3 on second roll

The probability of rolling a 3 on the second roll is also $\frac{1}{6}$ as the rolls are independent events.

Step3: Probability of both events

For independent events $A$ and $B$, the probability of both $A$ and $B$ occurring is $P(A\cap B)=P(A)\times P(B)$. Here, $A$ is the event of rolling a 3 on the first roll and $B$ is the event of rolling a 3 on the second roll. So $P(A\cap B)=\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}$.

Answer:

C. $\frac{1}{36}$