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

Explanation:

Step1: Find probability of first - die roll

A die has 6 faces. The probability of rolling a 1 on the first die is $\frac{1}{6}$.

Step2: Find probability of second - die roll

The probability of rolling a 1 on the second die is also $\frac{1}{6}$ since the two die - rolls are independent events.

Step3: Use multiplication rule for independent events

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

Answer:

$\frac{1}{36}$