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lec6 - Bayes Rule Example 1 Treasure Hunt suppose that...

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Bayes’ Rule Example 1: Treasure Hunt: suppose that there are three closed boxes. The first box contains two gold coins, the second box contains one gold coin and one silver coin, and the third box contains two silver coins. Suppose that you select one of the boxes randomly and then select one of the coins from this box. For a problem like this, that consists of a step-wise procedure, it is often useful to draw a tree (a flow chart) of the choices we can make in each step. The diagram below shows the tree for the 2 steps of choosing a box first and choosing one of two coins in that box. 1

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Example: continued The lines are marked by the probabilities, with which each step is done: Choosing one box (at random) means, that all boxes are equally likely to be chosen: P ( B i ) = 1 3 for i = 1 , 2 , 3 . In the first box are two gold coins: A gold coin in this box is therefore chosen with probability 1. The second box has one golden and one silver coin. A gold coin is therefore chosen with probability 0.5.
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