Question
A single die is rolled twice. Find the probability of rolling a 3 the first time and a 5 the second time.
Question content area bottom
Part 1
Find the probability of rolling a 3 the first time and a 5 the second time.
enter your response here (Type an integer or a simplified fraction.)
Question content area bottom
Part 1
Find the probability of rolling a 3 the first time and a 5 the second time.
enter your response here (Type an integer or a simplified fraction.)
Answers
GPT-4o mini
To find the probability of rolling a specific number on a die, we start by recognizing that each number on a six-sided die has an equal probability of occurring.
1. The probability of rolling a 3 on the first roll is \( \frac{1}{6} \).
2. The probability of rolling a 5 on the second roll is also \( \frac{1}{6} \).
Since these two events are independent (the outcome of the first roll does not affect the outcome of the second roll), we multiply the probabilities of the two events:
\[
P(\text{rolling a 3 first and a 5 second}) = P(3) \times P(5) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}
\]
Thus, the probability of rolling a 3 the first time and a 5 the second time is \( \frac{1}{36} \).
1. The probability of rolling a 3 on the first roll is \( \frac{1}{6} \).
2. The probability of rolling a 5 on the second roll is also \( \frac{1}{6} \).
Since these two events are independent (the outcome of the first roll does not affect the outcome of the second roll), we multiply the probabilities of the two events:
\[
P(\text{rolling a 3 first and a 5 second}) = P(3) \times P(5) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}
\]
Thus, the probability of rolling a 3 the first time and a 5 the second time is \( \frac{1}{36} \).