Probability - determine the probability for an event I have this probability question from homework
A system consists of $N$ chips in a parallel way, such that if at least one of the chips are working the system fully operates.
The probability that throughout a work day, a chip will get broken is $\frac{1}{3}$
Note that each of the events, where a chip is broken is an independent event.
At the end of a work day, the system still operates.
What is the probability that chip number 1 is operating (not broken)?
I struggle with understanding how I should approach this, because it seems at first sight that if the events are independent and we have the probability that each chip will be broken, then we could calculate the complement and get the probability that a chip still operates at the end of the day $(1-\frac{1}{3}) = \frac{2}{3}$
But I know it's wrong because I didn't consider all the other events in my calculation which I find hard to do.
Can I get some help how should I approach this?
Thanks.

Hint: use Bayes theorem which is mathematically given by: $$P(E_i\mid A)=\frac{P(A\cap E_i)}{P(A)}$$ where $E_i$ is one of the event occured from $E_1,E_2,...,E_n$ so can you find it now. 
$E_1$ here is: chip $1$ is working.
