Question

A large company has an inspection system for the batches of small compressors purchased from vendors. A batch typically contains 15 compressors. In the
inspection system, a random sample of 5 is selected and all are tested. Suppose there are 2 faulty compressors in the batch of 15.
(a) What is the probability that for a given sample there will be 1 faulty compressor?
(b) What is the probability that inspection will discover both faulty compressors?

Answer 1

Solution :

Given data :

Total number compressors in a batch = 15 compressors

Number of samples to be tested = 5

Let the number of faulty compressors out of 15 compressors = 2

a) Therefore, the ways of selecting $1$ faulty and $4$ good compressor is

$=^2C_1 \times ^{13} C_4$

The total number of ways = $^{15}C_5$

Therefore, the probability is

$=^2C_1 \times ^{13}C_4 \times ^{15} C_5$

$=0.4761$

b). Number of ways for selecting $2$ faulty and $3$ good compressor is

$^{13}C_3$

Thus the probability

$=\frac{^{13}C_3}{^{15}C_5}$

$=0.0952$