To calculate the probability of showing a 4 on both rolls of a die, let's first break it down:

• The probability of rolling a 4 on a single roll of a fair six-sided die is $\frac{1}{6}$, since there is only one outcome (a 4) out of six possible outcomes (1, 2, 3, 4, 5, 6).
• Since the die is rolled twice and the two rolls are independent events, the probability of rolling a 4 on both rolls is the product of the individual probabilities:

$\text{Probability of two 4s} = \frac{1}{6} \times \frac{1}{6} = \frac{1}{36}$

Thus, the probability of rolling a 4 on both rolls is $\frac{1}{36}$.

Would you like more details or have any questions?

Here are five related questions to explore further:

1. What is the probability of not rolling a 4 on either of the two rolls?
2. What is the probability of rolling a 4 on at least one of the two rolls?
3. If the die is rolled three times, what is the probability of getting a 4 on all three rolls?
4. How would the probability change if you were rolling an 8-sided die instead of a 6-sided die?
5. What is the probability of rolling two different numbers on the two rolls?

Tip: For independent events, always multiply the probabilities of each event to find the overall probability.