A list of the worlds 10 largest companies in terms of values

A list of the world\'s 10 largest companies, in terms of values, contains 5 from the United States, 3 from China, and 1 each from Germany and the Netherlands. A potential investor randomly selects 3 of the companies to research further.

Let X be the number of United States companies selected. Determine the mean and variance of X.

Solution

Here, there are

N = 10 companies
K = 5 US companies
n = 3 companies sampled

Thus,

Mean = nK/N = 3*5/10 = 1.5 [ANSWER]

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Meanwhile,

variance = n K(N-K)(N-n) / (N^2 (N-1))

= 3*5*(10-5)*(10-3)/(10^2*(10-1))

variance = 0.583333333 [ANSWER]