How to calculate needed sample size

I have a probability of an infection happening as 0.0001

I need to find exactly how many patients would have to come in to have the chance of an infection being 50%

I did it on my calculator and its somewhere between 6,800-7,000 but I need the matlab code to determine the exact number.

Answer 1

[Walter Roberson]

Remember,

Probability of an event occurring at least once in n tries is 1 minus the probability that the opposite event happens every time for n tries. Probability that the opposite event happens every time is (1-p)^n, so overall probability is 1 - (1-p)^n

For 50% chance you want the result to equal 1/2, 1 - (1-p)^n == 1/2 . So (1-p)^n == 1 - 1/2 .

Now take the log of both sides: n * ln(1-p) == ln(1/2) . Divide: n = ln(1/2) / ln(1-p) .

Now implement in MATLAB.