A batch of 10 fuses contains three defective ones. A sample of size two is taken at random and without replacement. (a) Find the probability that the sample contains no defective fuses. (b) Let X be...

A batch of 10 fuses contains three defective ones. A sample of size two is taken at random and without replacement.

(a) Find the probability that the sample contains no defective fuses.

(b) Let X be the random variable denoting the number of defective fuses in the sample. Find the probability mass function of X.

(c) Given that X = 1, what is the probability that the defective fuse was the first one selected?