A probability problem by Ritam Podder

There are 3 coins in a box. The probability of getting head is 2 3 \frac{2}{3} for two of them, while for remaining it is 1 2 \frac{1}{2} . A coin is chosen random and tossed 3 times, showing head in each case. What is the probability that the coin is unbiased?

1 2 \frac{1}{2} 1 32 \frac{1}{32} 3 11 \frac{3}{11} 27 155 \frac{27}{155}

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