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, 9 of which have electrical defects and 16 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 an electrical defect?

c)If a sample of 5 keyboards is randomly selected, what is the probability that at least 4 of these will have a mechanical defect? (Round your answer to four decimal places.)

Explanation / Answer

There are 25 failed keyboards out of which 9 have electrical defects and 16 have mechanical defects.

a) Since 5 keyboards need to be selected out of 15, this can be done in 25C5 ways.

25C5 = 53130.

b) The two keyboards with electrical defect can be chosen out of 9 in 9C2 ways. The remaining 3 can be chosen out of 16 in 16C3 ways.

Total number of ways = 9C2 * 16C3

= 20160.

c) The number of ways to select 5 keyboards, all of which have mechanical defect

= 16C5

= 4368.

The number of ways to select 4 keyboards with mechanical defect and 1 with electrical defect

= 16C4 * 9C1

= 1820 * 9

= 16380.

=> Probability that at least 4 of these will have a mechanical defect

= (4368 + 16380) / 53130

= 0.3905.

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