Tuesday, February 28, 2012

Unbiased decision from biased coin

You are given biased coin. Find unbiased decision out of it?


When we have a biased coin, then the probability of a head and a tail is not the same. Let us say the probability of coming up with a head(H) is p, so the the probability of tail(T) would be 1-p. The dice would be biased when p > 0.5 or vice-verse.
The task at hand is to stimulate a condition where the probability of occurrence of two events is the same. That cannot be done with a single toss of the dice, so we need to think a little out of the box.
Throw the biased coin twice.

Classify it as true for HT and false for TH. Both of these occur with probability=p*(1-p), and hence unbiased.
Ignore the other 2 events namely HH and TT.

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