Suppose that a die has n sides numbered i = 1, 2,, n. Assume that the probability

Question:

Suppose that a die has n sides numbered i = 1, 2,···, n. Assume that the probability of it coming up on the side numbered i is the same for each value of i. The die is rolled n times (assume independence) And a “ match” is defined to be the occurrence of side i on the ith roll. Prove that the probability of at least one match is given by