Question

You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. you choose a coin at random and toss it, and it comes up heads. the probability that the other face is tails is

Answer 1

This is textbook example of Bayes theorem. This theorem is useful whenever you are asked to compute an inverse probability. Here, you are asked the probability of other side being tails, given that one side is heads. Put other way, what is the probability that I had selected the coin with each side different, given that I have heads. Note that the inverse, i.e. “what is the probability of getting heads if I select the coin which has two sides different” is much simpler. Which means that Bayes’ theorem will come to our rescue:

Here Pr(H ) = Probability of choosing the coin with two faces heads and tails

Pr(O) = Probability of seeing heads up

Substituting:

Pr(H/O) = (1/2 * 1/3) / (1/3 * 1 + 1/3 * 0 + 1/3*1/2)

= (1/6) / (1/2)

= 1/3

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Answer 2

Answer:

You are given three coins: one has heads on both faces, the second has tails on both faces, and the third has a head on one face and a tail on the other. you choose a coin at random …