Question

A single die is rolled twice. Find the probability of getting a 5 the first time and a 5 the second time.

Answer 1

To find the probability of rolling a 5 on a single die twice, we first determine the probability of rolling a 5 on one roll of a die.

When rolling a standard six-sided die, there are 6 possible outcomes: 1, 2, 3, 4, 5, and 6. The probability of rolling a 5 on one roll is:

\[
P(\text{rolling a 5}) = \frac{1}{6}
\]

Since the rolls are independent events, the probability of rolling a 5 on both the first and the second roll is the product of the probabilities of each individual roll. Thus, we have:

\[
P(\text{rolling a 5 on first roll and a 5 on second roll}) = P(\text{rolling a 5 on first roll}) \times P(\text{rolling a 5 on second roll})
\]

Substituting the probabilities:

\[
P(\text{5 on first roll and 5 on second roll}) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}
\]

Therefore, the probability of getting a 5 the first time and a 5 the second time is:

\[
\frac{1}{36}
\]