An email spam filter correctly classifies mails (i.e. a spam mail as spam, a not-spam as not-spam) 2/3 of the times. Classification decisions are independent of each other. You test the classifier with a set of 3 emails. The classifier will stop when it performs one wrong classification (e.g. when it says that a spam email is not spam, or vice-versa), or when it correctly classifies all 3 emails.
** I have first done the binomial way. since they are asking for at most one so its 0 and 1.
$ \binom{3}{0}= \frac{3!}{0!(3!)} \cdot \frac{2}{3^0} \cdot \frac{1}{3^3} = 0.03703 $
$ \binom{3}{1}= \frac{3!}{1!(2!)} \cdot \frac{2}{3^1} \cdot \frac{1}{3^2} = 0.22222 $
when i add both of them i get 0.25925.
is this correct?
Thank you in advance