Final answer:
The probability of rolling a 4 on the first roll and not getting a 6 on the second roll of a fair six-sided die is found by multiplying the individual probabilities of each event, resulting in 5/36. Thus, the correct answer is 5/36, which corresponds to option 2.
Step-by-step explanation:
To find the probability of getting a 4 on the first roll and not getting a 6 on the second roll of a fair six-sided die, we can calculate these probabilities independently and then multiply them together since the rolls are independent events.
The probability of rolling a 4 on a fair die is 1/6 because there is only one 4 in a set of six possible outcomes. To not get a 6 on the second roll means we want one of the other five possible outcomes, so the probability is 5/6. Multiplying these together, we get:
Probability of rolling a 4 on the first roll = 1/6
Probability of not rolling a 6 on the second roll = 5/6
The combined probability is therefore (1/6) × (5/6) = 5/36.
Thus, the correct answer is 5/36, which corresponds to option 2.