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

#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

Let's go through each question one by one and explain how to calculate the probabilities.

a. What is her probability of each of the following?
1. Getting every note right.
To find the probability of getting every note right, you need to multiply the probability of getting a single note right by itself for each note in the solo. Since Clara's probability of playing any one note right is 99% (or 0.99), you can calculate the probability of getting every note right as follows:
0.99^60 ≈ 0.547

2. Making exactly one mistake
To calculate the probability of making exactly one mistake, you need to consider that there are 60 notes in total. You can choose one note to be the one Clara will get wrong, and the rest (59 notes) will be correct. The probability of getting one note wrong is 0.99, and the probability of getting 59 notes right is 0.99^59. Since there are 60 ways to choose the note that Clara will get wrong (combination of 60C1), you can calculate the probability as follows:
60C1 * (0.99)^1 * (0.99)^59 ≈ 0.369

3. Making exactly two mistakes
Similarly to the previous question, to calculate the probability of making exactly two mistakes, you need to choose two notes to be the ones Clara will get wrong, and the rest (58 notes) will be correct. The probability of getting two notes wrong is (0.99)^2, and the probability of getting 58 notes right is (0.99)^58. Since there are 60 ways to choose the two notes that Clara will get wrong (combination of 60C2), you can calculate the probability as follows:
60C2 * (0.99)^2 * (0.99)^58 ≈ 0.230

4. Making at least two mistakes
To calculate the probability of making at least two mistakes, you need to consider all possibilities where Clara makes two or more mistakes. This can be calculated by subtracting the probability of getting everything right and making exactly one mistake from 1.
1 - (probability of getting everything right + probability of making exactly one mistake)
1 - (0.99^60 + 60C1 * (0.99)^1 * (0.99)^59) ≈ 0

5. Making more than two mistakes
To calculate the probability of making more than two mistakes, you need to subtract the probability of getting everything right, making exactly one mistake, and making exactly two mistakes from 1.
1 - (probability of getting everything right + probability of making exactly one mistake + probability of making exactly two mistakes)
1 - (0.99^60 + 60C1 * (0.99)^1 * (0.99)^59 + 60C2 * (0.99)^2 * (0.99)^58) ≈ 0

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?
To find the probability of Clara getting all 60 notes right with a 95% probability, you need to solve for the probability of getting a single note right (let's call it x) in the equation:
x^60 = 0.95
To solve this, you take the 60th root of 0.95:
x = 0.95^(1/60) ≈ 0.9991454771