Question

A fair die with sides numbered 1, 2, 3, 4, 5, and 6 is to be rolled until a number greater than 4 first appears. what is the probability that a number greater than 4 will first appear on the third or fourth roll

Answer 1

First two rolls have to be 1-4 that is 2/3 chance twice and the third can be 4or 5
2/3*2/3*1/3 + the chance that the fourth is the 5 or 6. 
2/3*2/3*2/3*1/3

So the solution is : P=2/3*2/3*1/3 + 2/3*2/3*2/3*1/3