How likely is it that in five randomly-generated single-digit numbers there will be three of the same in a row? A random number generator creates five single-digit numbers. It produces the numbers 7, 5, 2, 2, 2.
How likely is it that in any set of five randomly generated single-digit numbers (0-9) there will be three or more identical ones? How likely is it that there will be three or more in a row?

For the second problem I come to: $$10\times P\left(A_{3,5}\right)=10\times10^{-3}\left(1+\left(5-3\right)\frac{9}{10}\right)=28\times10^{-3}$$
This on base of this question that was once asked by myself.
Also have a look at this question.
