TITLE: Probability of an event occuring at least once in 50 tries
QUESTION [7 upvotes]: Probability of an event is $.116$. In $50$ tries, what are the chances at least one event occurs? I see that the probability that it wouldn't happen in one try is $.884$ and the probability that it wouldn't happen in two tries is $(.884)^2$.

REPLY [7 votes]: If an event occurs $0$ times (out of $50$, in this case) then it does not occur at least once. So we can find the probability of it not occurring and then subtract that value from $1$. 
So, what are the chances of it not occurring on $1$ trial? $1-.116 = .884$
What about not occurring on $2$ trials? $(1-.116)\cdot (1-.116)=.884 \cdot .884 = .781456$
Now what about not occurring on $50$ trials? $.884^{50} \approx .002102$
We must subtract this value from $1$ (recall that what we just calculated is the probability of it not occurring, so the probability of it occuring at least once is:  $$1-.002102 \approx .9979 $$