It can be shown using mathematical induction and the formula P(A union B)=P(A+P{

Question

It can be shown using mathematical induction and the formula P(A union B)=P(A+P{B)-P(A intersection B), that if A_1, A_2, ..., A_n are events, then This is known as the inclusion-exclusion principle. Here is a famous probability problem: A professor returns exams to a class of n students by returning them in random order. Find the probability that no student gets their own exam returned to them? Let X_i equal 1 if the ith student gets their own exam back, and 0 otherwise. What does the random variable Y=X_1+X_2+...+ X_n represent? Find EY.

Explanation / Answer

A. There is only one way in which everyone will get their right exams.

So the total no.of ways in which students get wrong exams = n(n-1) - 1

Hence probability = (n(n-1) -1)/(n(n-1))

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