For a binomial r.v. "X" where:<br><br> p = The probability of success<br> k = The number of successes under consideration<br> n = The total number of trials<br><br> P{X = k + 1} = [p/(1-p)]*[(n-k)/(k+1)]*P{X = k}
<br><br> Using this relation one can calculate the probability of e.g. an N-K erasure coded file on a network with servers whose individual reliabilities (i.e. probability of<br>availability) are independently "p".
<br> Interestingly it requires no use of choose functions,<br>and a single use of floating points that are raised to large<br>powers, so the error term should be quite small, relative to the naive calculation. I wrote an ugly
<br>function that calculates the relevant Cumulative Distribution Function. Perhaps I should cut-n-<br>paste the monster here? <br><br> Would it be pedantic to go through calculating the<br>prob. and erasure coded file is available?
<br><br>Tersely: Start with P{X = 0} and work from there.<br>Then use 1 - P{file unavailable}. <br><br>--Cheers<br>arc<br>