A box contains $3$ coins . Among these three , each of two coins have the probability of giving head $\dfrac 23$ and the remaining one have the probability of turning head $\dfrac 12$ . One coin is chosen randomly from the box and tossed three times and each time it turns out to be head . What is the probability that the coin chosen from the box was the unbiased one i.e. the one with head probability $\dfrac 12$ ?
2026-03-31 20:04:19.1774987459
A Bayesian problem of coin tossing
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Hint:
Probability that you select a biased coin is $\frac23$. Probability of a biased coin coming up HHH in three tosses is $\frac{8}{27}$.
Probability that you select the unbiased coin is $\frac13$. Probability of the unbiased coin coming up HHH in three tosses is $\frac18$.
See if you can take it from here!