Weird coins!

Probability Level pending

There are three coins in a box. The probability of getting a head is 2 3 \frac23 for two of them, while for the remaining one, it is 1 2 \frac12 . A coin is chosen at random and tossed three times, showing head in each case. What is the probability that the coin is unbiased?

27 155 \frac{27}{155} 1 3 \frac13 1 8 \frac18 1 2 \frac12 3 8 \frac38

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