Shortly after being put into service, some buses manufactured by a certain compa

Question

Shortly after being put into service, some buses manufactured by a certain company have developed cracks on the underside of the mainframe. Suppose a certain city has 25 of these buses, and cracks have actually appeared on 8 of them. How many ways are there to select a sample of 5 buses from the 25 for a thorough inspection? In how many ways can a sample of 5 buses be chosen at random containing of exactly 4 with cracks? If a sample of 5 buses is chosen at random, what is the probability that exactly 3 of the five buses will have cracks? If a sample of 5 buses s chosen at random what is the probability that at least 4 of the 5 buses chosen have cracks?

Explanation / Answer

(a)

Since order of selection does not matter so number of ways of selecting 5 buses out of 25 is

C(25,5)= 53130

(b)

There are 8 buses with cracks and 17 without cracks so number of ways of selecting 4 buses from 8 buses with cracks and 1 out of 17 is

C(8,4)C(17,1) = 1190

(c)

Number of ways of selelcting 3 buses wth cracks is

C(8,3)C(17,2) = 7616

So requried probability is

7616 / 53130 = 0.1433

(d)

Number of ways of selelcting 4 buses or 5 buses with cracks is

C(8,4)C(17,1)+C(8,5)C(17,0) = 1246

So requried probability is

1246 / 53130 = 0.0235

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