p = 1/6
you roll a die and wait for the number 5 on the die.
Instead consider what is the probability of NOT getting a 5. It is 5/6 if you do that n times you have (5/6)^n.
Hence, the probability of getting at least one 5 is 1-(5/6)^n
We want this to be expected, i.e,
1-(5/6)^n >= 1/2
Thus,
(5/6)^n <= 1/2
Find the first value of n which makes this true.