-/3 points DevoreState 2 E.034 My Notes Ask Your Teacher + Computer keyboard fai

Question

-/3 points DevoreState 2 E.034 My Notes Ask Your Teacher + Computer keyboard failures can be attributed to electrical defects or mechanical defects. A repair facility currently has 25 failed keyboards, 10 of which have electrical defects and 15 of which have mechanical defects (a) How many ways are there to randomly select 7 of these keyboards for a thorough inspection (without regard to order)? ways (b) In how many ways can a sample of 7 keyboards be selected so that exactly two have an electrical defect? ways (c) If a sample of 7 keyboards is randomly selected, what is the probability that at least 6 of these will have a mechanical defect? (Round your answer to four decimal places.)

Explanation / Answer

a) Number of ways to slect 7 of these keyboards = 25C7 = 25! / (7! * (25-7)!) = 480700

b) Number of ways to have exactly two electrical defect = 10C2 * 15C5 = 45 * 3003 = 135135

c) P(at least 6 will have mechanical defect) = P(6 mechanical defect) + P(7 mechanical defect)

                                                = (15C6 * 10C1 / 25C7) + (15C7 / 25C7)

                                                = 50050/480700 + 6435/480700

                                                = 0.1175

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