Probability of event A when given percentage. $38\%$ of students are female, and I was asked to find the probability that the class valedictorian is a female. I figure $38\%\rightarrow$ woman then $62\% \rightarrow$ are male. To make it simple I made the sample size of $100$ students. So $38$ are woman and $62$ are male. Does that mean that there is a $38 \%$ chance the valedictorian is a female? Or is this more complicated than it seems? Edit: There's more to the problem. * What is the probability that $6$ out of the $10$ students are female? * How many females would be expected in the top $10$?

Your correct if that's the full stated question. This can become more complicated with hidden assumption i.e. rate of academic success of male vs female which we assume to be equal here. Also it doesn't take into account other categories based off the fact that female male is never a true real split. Further one could do math based off of the fact that we would expect 50% females and only have 38% which would imply that males perform better in academia. But without more information 38% is the correct answer. the expected value for females in the top ten is 3.8 females. For more on the probability of 6 females check out Binomial distribution .