Among the three coins, one has head onboth the faces, the second the tails on both of the faces, and the third has a head on one face and a tail on the other. A coin is chosen random and tossed. The result is a head. What is the probability that the opposite face is a tail.?
Answers
Answer:
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:
Step-by-step explanation:
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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