Question

a single die is rolled twice. find the probability of rolling a 2 the first time and a 5 the second time. find the probability of rolling a 2 the first time and a 5 the second time. (type an integer or a simplified fraction.)

Explanation:

Step1: Probability of rolling a 2 first

A die has 6 faces. The probability of rolling a 2 on the first roll is $\frac{1}{6}$ since there is 1 favorable outcome (rolling a 2) out of 6 possible outcomes.

Step2: Probability of rolling a 5 second

The probability of rolling a 5 on the second roll is also $\frac{1}{6}$ as there is 1 favorable outcome (rolling a 5) out of 6 possible outcomes.

Step3: Use multiplication rule for independent events

Since the two rolls are independent events, the probability of both events occurring is the product of their individual probabilities. So the probability is $\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}$.

Answer:

$\frac{1}{36}$