70 students take a multiple choice test with 100 questions. Each question has 4 possible answers— a, b, c, d — and there is only one correct answer per question. Student 1 gets 22 wrong answers and Student 2 gets 19 wrong answers. What is the probability that Students 1 and 2 have 13 wrong answers that are the same (eg. both picked “c” when c is one of the three possible wrong answers to a question) out of the 100 questions?
Does the fact that Student 1 had 13 out of 22 wrong answers that were the same as Student 2’s wrong answers prove that the two students were cheating off each other’s tests?