A die is rolled twice. What is the probability of showing a 4 on both rolls?Your answer is

1. Break Down the Problem

To find the probability of rolling a 4 on both rolls of a die, we first need to recognize the total number of outcomes and the number of favorable outcomes.

2. Relevant Concepts

• A standard die has 6 faces, each face representing a number from 1 to 6.
• The probability of rolling any specific number (like 4) on one roll is $\frac{1}{6}$.
• Since the rolls are independent, the probability of both events (rolling a 4 on the first and the second roll) occurring is the product of their individual probabilities.

3. Analysis and Detail

1. Probability of rolling a 4 on the first roll: $P(4) = \frac{1}{6}$

2. Probability of rolling a 4 on the second roll: $P(4) = \frac{1}{6}$

3. Combined Probability: Since the two rolls are independent, the combined probability is: $P(4 \text{ on first roll and } 4 \text{ on second roll}) = P(4) \times P(4) = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}$

4. Verify and Summarize

We have calculated the probabilities for both rolls and confirmed that they are correct. The combined probability indicates that there are 36 total possible outcomes when rolling a die twice, and only one of those would yield a (4, 4) outcome.

Final Answer

The probability of showing a 4 on both rolls is $\frac{1}{36}$.