Computer keyboard failures can be attributed to electrical defects or mechanical

Question

Computer keyboard failures can be attributed to electrical defects or mechanical defects. A repair facility currently has 25 failed keyboards, 12 of which have electrical defects and 13 of which have mechanical defects.

(a)

How many ways are there to randomly select 6 of these keyboards for a thorough inspection (without regard to order)?

1 ways

(b)

In how many ways can a sample of 6 keyboards be selected so that exactly two have an electrical defect?

2 ways

(c)

If a sample of 6 keyboards is randomly selected, what is the probability that at least 5 of these will have a mechanical defect? (Round your answer to four decimal places.)

3

Explanation / Answer

Ans:

a)There are 25C6 ways are there to randomly select 6 of these keyboards for a thorough inspection.

25C6=(25*24*23*22*21*20)/(6*5*4*3*2*1)=177100

b)12C2*13C4

=(12*11/2*1)*(13*12*11*10/4*3*2*1)

=66*715

=47190

c)Probability of getting mechanical defect=13/25=0.52

Probability of getting electrical defect=12/25=0.48

P(k>=5)=6C5*0.525*0.48+6C6*0.526

=0.1293

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