what is the probability of rolling a six on the first die and a six on the second die? write your answer as…

Explanation:

Step1: Probability of rolling a six on first die

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

Step2: Probability of rolling a six on second die

The probability of rolling a six on the second die is also $\frac{1}{6}$ for the same reason as the first die.

Step3: Use multiplication rule for independent events

Since the rolls of the two dice are independent events, the probability of both events occurring is the product of their individual probabilities. So $P(\text{six on first and six on second})=\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}$.

Answer:

$\frac{1}{36}$