Math
posted by Fiscars on .
There are 100 fish species that I have to be able to identify in a lab exam. I only had enough time to recognize 50 species. On the exam, they will randomly select 25 of the 100 species for testing. What's the probability or chance that I would be able to score 50% in that exam? How about 100%?

The probability of getting them all wrong is (50/100)*(49/99)*(48/98)*...(26/76)
= (50!/25!)/(100!/75!)
= 5.2*10^10
The probability is 50% for the first one, but keeps getting lower as a higher fraction of fish you know are left after each question.
The probablility of getting them all right is the same.
This assumes that the test is not multiple choice, in which case the scores tend to be higher due to lucky guesses.