I have the following function in Julia which calculates a certain probability.

function p(x, n)
    q = floor(Int, (n - 1) / 2)
    pr = 0
        for i in 1:q
            pr += (-1) ^ (i - 1) * binomial(q, q - i) * max(1 - i * x / q, 0) ^ (q - 1)
        end
    return pr
end

However, it seems that there is a problem when x is close to 0. The function returns values that are greater than 1 when x is close to 0. For example, the result of p(.1, 100) is 1.0225245327404304 but the value should never be greater than 1 since this value is a probability. Is this caused by computation errors? If yes, which part of the function causes this and how could I create a function that calculates the probability correctly?

Any help is much appreciated!