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.
