Question

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

(a) In how many ways can a sample of 7 keyboards be selected so that exactly two have an electrical defect?

(b) 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.)

Answer 1

Define events:

N represents the total number of failed keyboards (equal to 25).

X represents the total number of failed keyboards have electrical defects (equal to 13).                            

Y represents the total number of failed keyboards have mechanical defects (equal to 12).

(a): Total number of keyboards to be selected is 7.

Number of keyboards with electrical defects is C(13,2).

Number of keyboards with mechanical electrical defects is C(12,5).

The number of ways in which sample of 7 keyboards can be selected so that exactly two have an electrical defect is given by,

Therefore, the number of ways in which sample of 7 keyboards can be selected so that exactly two have an electrical defect is 61776.

(b): In this case we, have to select a sample of 7 defective keyboards, so that at least 6 of these will have a mechanical defect. The probability of this case can be determined by taking the sum or total of two events- one is exact number of 6 keyboards having mechanical defects and the other is all 7 keyboards having mechanical defects.

Therefore, the probability that at least 6 keyboards will have a mechanical defect out of the sample of 7 keyboards is 0.0266.