Information in condensed form:
=> Student takes 20 questions true or false exam.
=> He knows answer to 10 questions.
=> He guesses on 10 questions.
=> Professor randomly picks two questions out of 20, and finds student answered them both correctly.
Task: Find probability student knew answer to at least one of the two questions.
Bayes' Rule and conditional probability definition.
The Attempt at a Solution
My work. I found P(K|C) = 2/3 via Bayes' rule, where K: student knows answer, C: he got it correct. However I'm not sure how to tackle "at least 1" part of problem. My thoughts were pick c1, c2 element of C and find P(K|(c1 or c2)), but this seems like a difficult calculation.