Question

A typist types letters and envelopes to n different persons. The letters are randomly put into envelope. On the average, how many letters are put into their envelopes?

Answer 1

The problem of determining the average number of letters correctly placed in envelopes is related to the derangement problem in probability, with an expected value of 1 regardless of the number of persons n.

Step-by-step explanation:

The question describes a scenario where a typist types letters and envelopes for n different persons, and the letters are randomly placed into envelopes. The average number of letters correctly matched with their envelopes is sought. This is a classical problem in probability, known as the derangement problem or hat-check problem, and it involves factorial calculations and permutations.

The expected number of letters correctly matched, on average, is always 1. This is because the probability of a single letter being correctly placed is 1/n, and since there are n letters, the expected value is the sum of these probabilities, which is 1. This concept can be applied generally and is independent of the value of n.