A multiple choice exam has 10 questions. Each question has 4 possible answers, of which one is correct. A student knows the answers to 3 of the questions and answers them correctly. The student guesses the answers to the remaining 7 questions at random.
What is the chance the student answers exactly 7 of the 10 questions correctly?
Given that an answer is correct, what is the chance the student was merely guessing the answer?