Final answer:
The probability of rolling an odd number and then rolling a number greater than 1 on a six-sided die is 5/12.
Step-by-step explanation:
The student is asking about the probability of rolling a die with two specific outcomes occurring in sequence. Given a fair, six-sided die, we want to calculate the probability of rolling an odd number first and then rolling a number greater than 1. There are three odd numbers on a die: 1, 3, and 5. So the probability of rolling an odd number (event A) is 3 out of 6, or 1/2. The probability of rolling a number greater than 1 (event B) is 5 out of 6, because the numbers 2, 3, 4, 5, and 6 all satisfy this condition.
According to the product rule, the probability of two independent events A and B both occurring is the product of their individual probabilities. The sample space for this two-step process has 36 outcomes (6 outcomes from the first roll multiplied by 6 outcomes from the second roll).
So, the probability of rolling an odd number and then rolling a number greater than 1 is:
P(A and B) = P(A) \(times) P(B) = (1/2) \(times) (5/6) = 5/12.
Therefore, the requested probability is 5/12.