# Probability in selected group

35% of students are female. We know that if we select 20 from 200 students there are first 5 students who are male. What is a probability that 6th one is also male?

First of all, I don't know if I understand "We know that if we select..." part, does this imply always? My understanding of that part is "We already selected 20 of 200 and first 5 students were male".

My solution is that I ignore group and order part, because in my opinion if we selected 200 of 200 it would not change probability of 6th being male. So simply, probability of randomly selected student being male before is $\frac{130}{200}$ , we know already 5 are male so probability of next one is $\frac{125}{195}$

Do you think can I ignore the group and order part?

• Unfortunately I share in your confusion. Other interpretation: they selected one by one (planning to select $20$ in total) and the first $5$ were male. Then $195$ remain and $70$ or them are female. Probability for $6$-th selected student to be male: $\frac{125}{195}$. – drhab May 5 '16 at 12:43

It means that whatever you do, the first $5$ students are going to be male, so out of $130$ males, we already selected $5$, so we have $125$ males remaining and $70$ females, in the next selection, probability of selecting a male student would just be = $\frac{125}{195}$