You have a deck of 50 cards with 4 aces in it. I want to calculate the probability that you will get at least one ace when you draw 3 random cards from the deck without replacement. So, I did the following: (4/50)+(4/49)+(4/48) = .2449659864 Now I wanted to also calculate the probability that there will be no aces in the 3 random cards using the same way. I could have just subtracted the number I got from 1 but I wanted to do it the same way, so I did: (46/50)*(45/49)*(44/48) = .7744897959 The only problem is that they don't add up to 1. When I even string the whole thing in my Ti 83+ I get 1.019455782 which is like a 2% difference. Is that just a calculator significant digits error? Did I do something wrong? I'm thinking the probability of 2 aces out of 3 cards and 3 aces might have to be included in there somehow but isn't that taken care of when I calculate the probability of at least 1 ace in the first step? Thanks.