Probability question

Question

Q: A sophomore class has 100 students sitting in a theater, 40% are girls. A blindfolded person picks 10 students at random from the class. The first 7 were boys, the next 2 were girls. What is the probability the 10th person will be a girl?

I know the P(.4)=40%, but what's the formula when only 10 are chosen, and we're down to the last student?

Answer 1

We start with 60 boys and 40 girls. 7 boys and 2 girls have been selected, so 53 boys and 38 girls remain. Thus, if we assume totally random selection, the probability that the tenth student is a girl is 38/(38+53) = 38/91 is approximately .4176. Note: the fact that 7 boys were selected, then 2 girls would lead me to believe that gender selection was not truly done at random, so we would need extra knowledge to answer the question.