Answer to Question #129078 in Statistics and Probability for Abdul Rehman

Question

There are 20 computers in a store. Among them, 15 are brand new and 5 are refurbished. Six computers are purchased for a student lab. From the first look, they are indistinguishable, so the six computers are selected at random. Compute the probability that among the chosen computers, two are refurbished.

Answer 1

Let the probability of selecting 6 out of 20 computers be denoted by Nt= (20 choose 6)

Let the probability that the probability that at least two computers are refurbished and four are brand new be denoted by Nr= (5 choose 2)*(15 choose 4)

Nt = nCr(20, 6)

Nr = nCr(5, 2)* nCr(15, 4)

P(two are refurbished) = Nr/Nt

$\therefore P(Two Are Refubished) =\frac{nCr(5, 2)* nCr(15, 4)} {nCr(20, 6)} = 0.3522$