Question

Please answer this with as much detail as possible so I can better understand it.

Thank you in advance!

A university student is writing a multiple-choice test with 20 questions. Each question on the test has 4 choices for an answer, one of which is the correct one. To pass the test, the student must get at least 50% of the answers correct. The student has absolutely no idea what any of the correct answers are, and so guesses on all of the questions. Calculate, to the nearest %, the probability that: a) the student passes the test. b) if the student writes 5 different tests like this, they would pass none of them. c) if the student were to write tests like this until they passed 1 of them, they would need to write more than 40 tests.

Answer 1