Question

a single die is rolled twice. find the probability of rolling a 3 the first time and a 5 the second time. find the probability of rolling a 3 the first time and a 5 the second time. (type an integer or a simplified fraction.)

Explanation:

Step1: Determine single - roll probabilities

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). Similarly, the probability of rolling a 5 on a single die roll is $\frac{1}{6}$.

Step2: Use the multiplication rule for independent events

Since the two die - rolls are independent events, the probability of both events occurring is the product of their individual probabilities. So, $P(3\text{ first and }5\text{ second})=\frac{1}{6}\times\frac{1}{6}$.

Step3: Calculate the final probability

$\frac{1}{6}\times\frac{1}{6}=\frac{1}{36}$.

Answer:

$\frac{1}{36}$