Computer keyboard failures can be attributed to electrical defects or mechanical defects. A repair facility currently has 25...?
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.)
- roderick_youngLv 72 months ago
It's important to know the function C(n,k), which is the number of ways k objects can be chosen out of n total objects. C(n,k) = n!/(k! (n-k)!) Look up Factorial if you don't know what the ! means.
a) Exactly 2 have an electrical defect. That means exactly 7 - 2 = 5 must have a mechanical defect. The number of ways to choose the 2 electrical defects out of the 13 available is C(13, 2) = 13! / (2! 11!) = 13 * 12 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 / (2 * 1 * 11 * 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) = 13 * 12 / 2 = 78
Similarly, you can figure out how many ways you could choose those 6 mechanical defects out of 12. That *might* be 800, but you'd BETTER DO THE WORK TO MAKE SURE.
So the number of ways to produce the desired combination is 78 * 800 = 62400
The probability of getting the desired combination is then 62400 divided by the total number of combinations.
The total number of ways to choose 7 keyboards out of 25, period, is C(25, 7), and you can work that out. I think it could be 8652600, but better check.
If all the calculations above were right, the probability would be 64200/8652600
b) Very similar to the previous problem. 6 or more mechanical defects out of 7 means 6 defects, or 7 defects. Calculate the probabilities for each using the method of part a), and add the two together.
- Anonymous2 months ago
a.) the number of ways in which sample of 7 keyboards can be selected so that exactly two have an electrical defect is 61776.
b.) the probability that at least 6 keyboards will have a mechanical defect out of the sample of 7 keyboards is 0.0266