Pez Boy wrote: > > My statistics textbook mentioned the following problem: "A secretary addresses > 50 different letters and envelopes to 50 different people, but the letters are > randomly mixed before being put into envelopes. What is the probability that at > least one letter gets into the correct envelope?" It said that the probability > was 0.632 but simply said that the solution was "way beyond" the scope of the > text and did not give a place to look for further information. Could someone > explain how to find this result or point me to a web site that explains it? > A wise Indian mathematician who visited our faculty a few years ago gave me some very useful advice, a good principle for problem-solving and lateral thinking. "To solve a complicated problem, try solving a simple problem first." So, a hint: Try calculating the probability that every letter finishes up in a WRONG envelope, by finding (a) the number of ways this can happen and (b) the total number of different ways all the letters could be placed in all the envelopes. Call this probability pw. (1 - pw) must therefore be the probability of every other combination, i.e. the probability that at least one letter is in its correct envelope. (Dr) Paul Gardner, Director, Research Degrees
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