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Probability

Probability

IP 4

A biased coin lands heads with probability \(p\). Two independent tosses produce exactly one head with probability \(\frac{12}{25}\).

  1. Form an equation in \(p\).

  2. Find all possible values of \(p\).

  3. Explain why there are two possible answers.

Solution:

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Answer:(a) \(2p(1-p)=\frac{12}{25}\). (b) \(p=\frac25\) or \(p=\frac35\). (c) Swapping the probabilities of heads and tails preserves the probability of exactly one head in two tosses.

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