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March 29, 2017

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Clara Nett is quite good and figures that her probability of playing any one note right is 99%. The solo has 60 notes.

a. What is her probability of each of the following?
1. Getting every note right.
My answer: 0.547

I am stuck on problems 2-5 because when I set up the nCx I got 0 for all the answers which is not sensable.....
2. Making exactly one mistake
3. Making exactly two mistakes
4. Making at least two mistakes
5. Making more than two mistakes
b. What must be Clara's probability of getting any one note right if she wants to have a 95% probability of getting all 60 notes right?
Is this the correct set up ?

x^60=0.95
My answer: 0.9991454771

  • Probability - ,

    #1 is correct, in effect what you are doing is

    C(60,60) (.99^60 (.01)^0 = .547

    #2, you want to have 59 correct and one wrong

    = C(60,59) (.99)^59 (.01)^1
    = 60(.55268..)(.01) = .33161

    #3 , same way, 58 correct, 2 wrong
    prob = C(60,58) (.99)^58 (.01)^2 = .09881

    #4 , at least 2 mistakes
    ---> making 2 mistakes + making 3 mistakes + .. + making 60 mistakes
    or 1 - making none - making 1

    = 1 - .547-.33161 = .12139

    #5 , making more than 2 mistakes
    ---> making 3 + making 4 + ... + making 60
    how does that differ from #4 ?

    b) to get a 95% we must have
    x^60 = .95
    take 60th root
    x = .95^(1/60) = .999145

    I think your problem is in evaluating something like

    C(60,58)
    by definition this is 60!/(58!2!)
    perhaps your calculator cannot carry those large numbers and overloads
    - most calculators have a function nCr
    on mine it is found along the "5" key and my keystrokes are:

    60
    2ndF
    5
    58
    = to get 1770

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