Problem 8: Computer keyboard failure can be attributed to electrical defects or

Question

Problem 8: Computer keyboard failure can be attributed to electrical defects or mechanical defects. A repair facility currently has 20 failed keyboards, 5 of which have electrical defects and 15 of which have mechanical defects (a) How many ways are there to randomly select 5 of these keyboards for a thorough inspection (without regard to order)? (b) In how many ways can a sample of 5 keyboards be selected so that exactly two have a mechanical problem? (c) If a sample of 5 keyboards is randomly selected, what is the probability that at least 4 of these will have an electrical defect?

Explanation / Answer

a)number of ways to select 5 out of 20 =20C5 =20!/(5!*(20-5)!)=15504

b)

P(2 with mechanical and 3 with electrical)=15C2*5C3/20C5 =0.0677

c)

P(at least 4 have electric defect)=P(4 have electric defect)+P(5 have electric defect)

=15C1*5C4/20C5 +15C0*5C5/20C5 =0.0048+0.0001 =0.0049

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