A box contains 55 balls numbered from 1 to 55. If 15 balls are drawn with replacement, what is the probability that at least two of them have the same number?

Answer 1

take prob that they are both different
first can be anything, the second must be one of the other 54
prob that they are both different = (1)(54/55) = 54/55

prob( they are NOT both different)
= prob(at least two are the same) = 1 - 54/55 = 1/55