How can I find the probability that 20 rolls of a die will give (a) at least one six?

Question

Also probability that 20 rolls of a die will give (b) three sixes
(c) one six, two fives and three fours.


Thanks

Answer 1

You have to calculate the probability that 20 rolls will _not_ give you a 6 and subtract that from 1.

For any given roll, the probability of not getting a 6 is 5/6.
For 20 rolls, your probability of not getting a 6 is 5^20/6^20 or about 0.026

The probability that you _will_ get a 6 then, is 1 - 0.026 or about 0.974.