Calculate the probability that you will be able to keep a gum ball on the first try.

A paper bag contains a mixture of three types of candy. There are ten gum balls, seven candy bars, and three packages of toffee. Suppose a game is played in which a candy is randomly taken from the bag and then a second candy is drawn from the bag, without replacement. You are allowed to keep both candies, if, and only if, the second is the same type as the first.

a) Calculate the probability that you will be able to keep a gum ball on the first try.

b) Calculate the probability that you will be able to keep any candy on the first try.

c) Calculate the probability that you will not be able to keep any candy on the first try.