Question

Please help me with this probability question :)

A student takes a true-false examination containing 20
questions. On looking at the examination the student and that he
knows the answer to 10 of the questions which he proceeds to answer
correctly. He then randomly answers the remaining 10 questions. The
instructor selects 2 of the questions at random and  that the students answered both questions correctly. What is the probability that
the student knew the answer to at least one of the two questions?

Answer 1

If the student got 2 questions correct, then he did not know the answers definitively with probability \(\cfrac{10}{20}\cfrac{9}{19}\). The compliment of this is the probability that he knew at least 1 of the questions definitively: \(1-\cfrac{10}{20}\cfrac{9}{19}=\cfrac{27}{38}\), with is about 71%.