Suppose there are 3 defective items in a lot (collection) of 50 items. A sample of size 10 is taken at random and without replacement. Let X denote the number of defective items in the sample. Find the probability that the sample contains

(a) Exactly one defective item.

(b) At most one defective item.

Step 1 of 4:

Given that a lot of 50 items contain 3 defective items. A sample of size 10 is chosen at random without replacement and X denotes the number of defective items in the sample.

Therefore X follows hyper geometric distribution with m=3,N=50 and n=10.

That is X~Hypergeometric (N=50,m=3,n=10).