$\begingroup$What is more probable; a single 50% chance at success, or ten 5% chances at success?
If the former, how many additional 5% chances are required in order for it to be as likely to succeed using multiple 5% chances?
$\endgroup$21 Answer
$\begingroup$The chance of at least no success in ten tries with probability $p$ is $(1-p)^{10}$ because you have to fail every time. The chance of at least one success is then $1-(1-p)^{10}$. Substituting in $p=0.05$ gives about $0.4013$. Your expectation is one half success, but there is a chance of more than one so the chance of at least one has to be lower. To find how many tries you need, increase the exponent $10$ until you get more than $1/2$
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