Math and Probability

Question

Some professors grade homework by choosing only a few problems to grade. On a 20-question homework, if you did 15 of the questions, and the professor picks 4 questions to grade, what is the probability that all of the ones they choose are ones you did?

Answer 1

15 done out of 20

4 chosen to grade

odds all 4 came from the 15 = 91/323= almost 30%

15/20 x 14/19 x 13/18 x 12/17

= 1/4 x 14/19 x 13/3 x 2/17

= 1/2 x 14/19x13/3 x1/17

=7/19x13/3 x1/17

= 91/19x3x17

=91/323

= about 28.17 % chance of all 4 from the 15