Question

A die is rolled 20 times. find the probability of getting exactly four two's out of 20 attempts.

Answer 1

First find the probability of getting four twos in a row.

(1/6)^4*(5/6)^16

Then you would multiply this probability by the number of combinations of those four twos in a sequence of 20 attempts

20!/(4!(20-4)!)

And the product of the probability times the number of combinations is:

(1/1296)(152587890625/2821109907456)4845 :P which is approximately:

0.2022 or 20.22% to the nearest hundredth of a percent.