Question

A single die is rolled 8 times. What is the probability that a six is rolled exactly once, if it is known that at least one six is rolled?

Answer 1

1 out of 8 dice is already know to be a six, so you have 7 unknown dice, each with a 5/6 chance of not rolling a six.

can you figure it out with that information?

Answer 2

Note that your sample space will be such that there is always a throw in which you have got 6.
so now keeping that in mind, simply calculate the probability. first find the probability that you didn't get any 6 after throwing a 6, this is the numerator and our denominator will contain (1 - probability of not getting 6 in the any throws). You will get the answer.