Probability, Statistics, May 1, 2019

General Thoughts
* Sometimes it is easier to calculate the “Not” case, rather than the “Success” case.

How to calculate a confidence interval for a population mean when you know its standard deviation

x_bar - simple mean or average
z - the percentage you want the confidence interval over, eg 0.90 for 90%
sigma - the know standard deviation
n - the count of samples
u - the confidence interval

u = x_bar +/- ( z * (sigma / sqrt(n) )

Probability of success after N tries

1 - (1 - P) ^ N

P = Probability of success
N = Number of tries

So if we have something that is 80% likely to succeed and we try the test 4 times:

1 - (1 - 0.8) ^ 4 = 0.9984

You have a 99.84% chance that at least one of the four attempts will succeed.

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What is the probability of any one of multiple things happening?

Say for example:
* The probability of an SP/DP failure is 6%
* The probability of a VP failure is 7%
* The probability of a FC/IO failure is 8%

From https://stats.stackexchange.com/questions/241018/probability-of-completing-n-events

Where the big Pi symbol is the product of all the elements from 1 to i

The “not” probabilities
* The probability of an SP/DP not failing is 100 - 6 or 94%
* The probability of a VP not failing is 100 - 7 or 93%
* The probability of an FC/IO not failing is 100 -8 or 92%

The probability that no event occurs is

0.94 * 0.93 * 0.92 = 0.804264

The probability that at least one event occurs is

1 - (0.94 * 0.93 * 0.92) = 1 - 0.804264 = 0.195736 or 19.5736%