Shortly after being put into service some buses manufactured

Shortly after being put into service, some buses manufactured by a certain company have developed cracks on the underside of the main frame. Suppose a particular city has 25 of these buses, and cracks have actually appeared in 8 of them.

A) How many ways are there to select a sample of 5 buses from the 25 for a thorough inspection?

B) How many 5-bus samples contain exactly 4 buses with visible cracks?

C) If a sample of 5 buses is chosen at random, what is the probability that exactly 4 of the 5 will have visible cracks?

D) If buses are selected as in part c, what is the probability that at least 4 of those selected will have visible cracks?

Solution

A)

Number of ways to select a sample of 5 buses from the 25 for a thorough inspection = 25C5

= 25!/(20!*5!)

=53130 Answer

B)

Number of 5-bus samples contain exactly 4 buses with visible cracks= 8C4*17C1 = 1190 Answer

Logic : Choose 4 from 8 cracked, 1 from 17.

C)

If a sample of 5 buses is chosen at random, the probability that exactly 4 of the 5 will have visible cracks

=1190 / 25C5

= 119 / 5313

= 0.0224 Answer....(divide B ans by total ways )

D)

Number of ways of selection = 1190 + 8C5 = 1246 ...[B ans + ways for all 5 cracked]

Probability = 1246 / 53130 = 0.0235 Answer