Fun with Coins
Answer these following questions about flipping a fair coin.
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What is the probability that you will throw Tails forever with a fair coin?
The probablity that you will throw \(n\) Tails in a row is \((\frac{1}{2})^n\). As \(n\) approaches infinity, the probability goes to 0.
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What is the probability that you will throw at least one Head when you keep throwing a fair coin forever?
This event happens exactly when you don't throw Tails forever. Since we know the probability of throwing Tails forever is 0 from the previous part, the probability of at least one Head is 1 - 0 = 1.