a) Colin's name is one of ten names. Two names are chosen (with possible repeat). What is the probability that
Colin's name chosen at least once.
Let's find the probability that his name is not chosen and then subtract that from 100%.
There are 9 out of 10 ways to not choose his name the first time and also, since that name is allowed to be
chosen again, 9 out of 10 ways to not choose his name the second time. This is: 9/10 x 9/10 = 81/100
for a probability of 0.81.
The probability that his name will be chosen at least once is 1.00 - 0.81 = 0.19.
b) Same situation but no name can be chosen twice.
The probability that his name won't be chosen the first time is 9/10. Since there are no repeats, the probability
that his name won't be chosen the second time is 8/9. This is 9/10 x 8/9 = 72/90 for a probability of 0.80.
The probability that his name will be chosen is 1.00 - 0.80 = 0.20.