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

Explanation:

Step1: Probability of first - die result

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

Step2: Probability of second - die result

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

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 $P(\text{2 on first and 1 on second})=\frac{1}{6}\times\frac{1}{6}$. $P(\text{2 on first and 1 on second})=\frac{1\times1}{6\times6}=\frac{1}{36}$

Answer:

$\frac{1}{36}$