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Korvikt [17]
3 years ago
5

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?
Business
1 answer:
zmey [24]3 years ago
3 0

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

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

$=0.0952$

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