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, 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)

Since order of keyboards is not important so number of ways of selecting 7 kerboards out of 25 is

C(25,7) = 480700

(b)

Number of ways of selecting 2 keyboards out of 10 that have electrical defects is

C(10,2) = 45

Number of ways of selecting 5 keyboards out of 15 that have mechanical defects is

C(15,5) = 3003

So number of ways can a sample of 7 keyboards be selected so that exactly two have an electrical defect is

45 *3003 = 135135

(c)

Number of ways of selecting 6 keyboards that have mechanical defects is

C(15,6) (10,1) = 50050

Number of ways of selecting 7 keyboards that have mechanical defects is

C(15,7) = 6435

So the number of ways of selecting at least 6 that have a mechanical defect is

6435 + 50050 = 56485

Therefore the probability that at least 6 of these will have a mechanical defect will be

56485 / 480700 = 0.1175

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