We have a fair six-sided die. When we roll it:
- There's a $1$ in $6$ chance $(1/6$ probability) of getting a '$1$' on the first roll.
- There's also a $1$ in $6$ chance $(1/6$ probability) of getting a '$4$' on the second roll.
Since these rolls are independent events, meaning one doesn't affect the other, we can multiply the probabilities:
$(1/6) * (1/6) = 1/36$
So, the probability of rolling a '$1$' on the first roll and a '$4$' on the second roll is $1/36.$
Correct Answer: A