A fair six-sided die is rolled twice. What is the probability of rolling a 6 on both rolls?

Step 1: Find the probability of rolling a 6 once.

A fair six-sided die has 6 equally likely outcomes, and only one outcome is a 6.

Therefore:
P(6) = 1/6

Step 2: Determine whether the rolls are independent.

The result of the first roll does not affect the result of the second roll, so the two rolls are independent.

For independent events, multiply their probabilities.

Step 3: Multiply the probabilities.

P(6 on both rolls) = (1/6)(1/6)

P(6 on both rolls) = 1/36

Step 4: Express the result as a decimal if desired.

1/36 ≈ 0.0278

Therefore, the probability of rolling a 6 on both rolls is 1/36, or approximately 0.0278.