Final answer:
The probability of not rolling two consecutive 6s on a 6-sided die is calculated by subtracting the probability of rolling two 6s (1/36) from 1, which results in 35/36.
Step-by-step explanation:
The question is about calculating the probability of not rolling two 6s successively on a fair, six-sided die. To find this probability, we note that the chance of rolling a 6 on a single roll is 1 in 6 (P(6) = 1/6). The event of rolling two 6s in a row is the product of the probabilities of each individual event, since each roll is independent. So for two rolls, P(6 and then 6) = P(6) × P(6) = (1/6) × (1/6) = 1/36. Now, to find the probability that this does not happen, we subtract the probability of the event from 1. So the probability of not rolling two 6s successively is 1 - P(6 and then 6) = 1 - (1/36) = 35/36. Therefore, the probability that you would fail to successively roll two 6s on a 6-sided die is 35/36.