Question

Many manufacturers have quality control programs that include inspection of incoming materials for defects. suppose a computer manufacturer receives computer boards in batches of five. two boards are randomly selected from each batch for inspection. consider batches for which exactly two of the boards are defective; for convenience, number the defective boards as 1 and 2, and the nondefective boards as 3, 4, and 5. let x denote the number of defective boards among the two actually inspected, and determine the mass function of x. hint: one possible sample of size 2 consists of boards 1 and 2, another of boards 1 and 3, and so on. how many such samples are there, and what is the value of x for each sample?

Answer 1

There are ten combihations of the 5 boards taken 2 at a time. The values of x for each combination are as follows:
(1 ,2), x = 2;  (1, 3), x = 1;  (1,4), x = 1;  (1, 5), x = 1;  (2, 3), x = 1;  (2, 4), x = 1;  (2, 5), x = 1;  (3,4), x = 0;  (3, 5), x = 0;  (4, 5), x = 0.
The mass function of x can be expressed as follows:
P(x = 0) = 0.3.
P(x = 1) = 0.6.
P(x = 2) = 0.1