monte_exceedance( p, h, runs )

function exc = monte_exceedance( p, h, runs )
%
% MONTE_EXCEEDANCE( P, H, RUNS ) calculates the probability of equaling or
% exceeding h hits for probabilities p (column vector). Uses a monte carlo method,
% as the author finds analytical statistics tiresome. This should reflect
% binomial distribution calculations for uniform p.
% 
% Example:
% There is a 30% chance of rain Saturday, and 20% Sunday. What is the
% probability that it rains this weekend?
% 
% monte_exceedance([.3; .2],1)
% 
% ans =
%     0.4431
% 
% Which is reasonably close to the theoretical value of .44

if nargin < 3
    runs = 10000;
end

r   = rand(length(p),runs);
exc = mean( sum(bsxfun(@lt,r,p)) >= h );

end