A company bought 30 new printers (15 black & white and 15 color printers). Later

Question

A company bought 30 new printers (15 black & white and 15 color printers). Later, circuit problems developed in 6 black & white printers and 3 color printers.

a) How many ways are there to select a sample of 6 printers from the 30?

b) If a sample of 6 printers is chosen at random, what is the probability that exactly 3 of the 6 will have circuit problems?

c) Now while randomly choosing 6 printers the technician decides to have at least 1 B&W printer and at least 1 color printer. What are the number of ways in which this can be done?

d) When the technician choses 6 printers as per the scheme in (c) what is the probability that all the printers are working perfectly fine?

Explanation / Answer

A) No of ways = 30C6 = 30! / (6! * 24!) = 593775

B) P (exactly 3 have circuit problem) = 9C3 * 21C3 / 30C6 = 128520 / 593775 = 0.22

C) No of ways = 1 - (15C6 + 15C6)

= 1 - 10010 = 10009

D) P(all the 6 printers are working perfectly fine) = (9C6 + 12C6) / 30C6 = 924 / 593775 = 0.002

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