Question

A corporation is sampling without replacement for n = 3 firms to determine the one from which to

purchase certain supplies. The sample is to be selected from a pool of six firms, of which four are

local and two are not local. Let Y denote the number of nonlocal firms among the three selected.

(a) P(Y = 1).

(b) P(Y ≥ 1).

(c) P(Y ≤ 1).

Answer 1

Let Y denote the number of nonlocal firmth among the three selected, then the random variable Y has a hyperhiometric distribution with N=6, r=2, n=3 . The probability distribution of Y is

$P(Y=y)=p(y)=\frac{(_y^r)(_{n-y}^{N-r})}{(_n^{N})}=\frac{(_y^2)(_{3-y}^{4})}{(_3^6)}$

a. $P(Y=1)=\frac{2\times6}{20}=0.6$

b.$P(Y ≥ 1)=p(1)+p(2)=0.6+0.2=0.8$

c. $P(Y ≤ 1)=p(0)+p(1)=0.2+0.6=0.8$