A shipment of 8 similar microcomputers to a retail outlet contains 3 that are defective. > A shipment of 8 similar microcomputers to a retail outlet contains 3 that are defective. If a school makes a random purchase of 2 of these computers, find the probability distribution for the number of defectives. Q: Is there a way to solve the above with Poisson distribution?

The Poisson distribution is neither called for nor effective here. The cases can be counted directly: 0, 1 or 2 computers will be defective. Labelling all the computers distinctly we have $\binom82=28$ choices.

For 0 defective computers we select any two of the five working computers: $\binom52=10$. For 2 we have three to select from: $\binom32=3$. By exclusion, the remaining $28-10-3=15$ choices have exactly 1 defective.

Thus there is a $\\{3/28,15/28,5/14\\}$ chance that $\\{0,1,2\\}$ computers will be defective - the desired probability distribution.