is 52 chances at 30/5,489,031,744 odds better then 1 chance at 1560/5,489,031,744 odds
or is it the same?
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1$\begingroup$ They are the same, assuming these are completely independent events (30*52=1560). $\endgroup$– user2974951Commented May 11, 2020 at 8:08
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$\begingroup$ Better in what sense? $\endgroup$– Peter FlomCommented May 11, 2020 at 12:05
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1 Answer
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They are almost the same, but I don't think they're quite exactly the same.
But we can check it using the binomial distribution. Let p denote the probability of success in 1 average chance.
Then $\mathbb{P}$(at least 1 success)$ = 1 - \mathbb{P}$(no successes)$ = 1 - (1-p)^{52}$.
The alternative is $52p$ for the higher chance probability.
Bernoulli's inequality says for $x \geq -1, (1+x)^n \geq 1+nx$.
So we know that $1-(1-p)^{52} \geq 1-(1-52p) = 52p$
SO the probability obtained from lots of smaller chances is almost the same as one larger chance (due to $p$ being so small), but there is a very very small difference between them.
