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Anonymous
Anonymous asked in Science & MathematicsEngineering · 2 months ago

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.)

2 Answers

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  • 2 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.

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  • Anonymous
    2 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

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