Introduction to Probability · Problem 8.1.11

Law of Large Numbers — Grinstead & Snell

Mathematics — Probability · law-of-large-numbers

Problem

We have two coins: one is a fair coin and the other is a coin that produces heads with probability 3/43/4. One of the two coins is picked at random, and this coin is tossed nn times. Let SnS_n be the number of heads that turns up in these nn tosses. Does the Law of Large Numbers allow us to predict the proportion of heads that will turn up in the long run? After we have observed a large number of tosses, can we tell which coin was chosen? How many tosses suffice to make us 95 percent sure?

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