There is a bag containing two coins: one double-headed and one coin which is weighted such...
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There is a bag containing two coins: one double-headed and one coin which is weighted such that the probability of getting heads when it is flipped is 75%. A coin is taken at random from the bag and flipped. If it lands heads, what is the probability that the coin is double-headed?
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Show answer & explanation
Using Bayes' theorem for consecutive heads observations, the posterior probability of the double-headed coin rounds to 63%.
Step-by-step Derivation:
Step 1: Prior probabilities P(C1) = P(C2) = 0.5.
Step 2: Likelihoods of getting heads: P(H|C1) = 1.0, P(H|C2) = 0.75.
Step 3: Over repeated trials yielding heads, the posterior probability P(C1|H) evaluates to approximately 63%.