a bag contains one fair coin, two two-headed coins, and three two-tailed coins. each of the...
a bag contains one fair coin, two two-headed coins, and three two-tailed coins. each of the is flipped, but the outcomes of the fice coins are hidden from you, randomly. if the outcome you see is headsm, what is the probability that the fair coin (which may or may not be the coin that was shown to you) panded heads up?
Homework Answers
For a fair coin, P(fair coin landed heads up) = 1/2.
If the fair coin landed heads up, there will be 3 coins which have landed heads up, so P(coin shown to us landed heads up) = 3/6.
If the fair coin did not land heads up, there will be 2 coins which have landed heads up, so P(coin shown to us landed heads up) = 2/6.
Thus, using Bayes' theorem, we have:
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