# Probability of independent not mutually exclusive events

I am wondering if I am doing this right. If an event has a probability of happening of $0.9\%$, what is the probability it will happen if it is repeated $50$ times. I have tried to calculate this with this formula:

$1-0.009^{50}$

Which gives $1$, so what I am wondering is it really true that if an event has a chance of only $0.9\%$ of happening once, if repeated $50$ times it will happen for sure, or have I used the wrong formula to calculate this?

• You have calculated that the event does not happen 50 times in 50 trials. – callculus Jul 25 '18 at 9:53

• $0.009^{50}$ is the probability the event happens $50$ times out of $50$
• $1-0.009^{50}$ is the probability the event happens fewer than $50$ times out of $50$
• $(1-0.009)^{50}$ is the probability the event happens $0$ times out of $50$
• $1-(1-0.009)^{50}$ is the probability the event happens more than $0$ times out of $50$
The chance of happening is $0.009$. So what do you compute by $$1-0.009^{50} ?$$ That is the chance that in 50 tries, it happens at most 49 times, and of course that is quite high, given the small chance.
What you need to compute is $$1 - 0.991^{50} \approx 36\%,$$ I'll leave it to you to find out why. :)
Because your calculator can only calculate up to certain precision. For a value that is too small, say $0.009^5$ in your case, the calculator regards it as $0$.