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 stepwise 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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 Spring '11
 Zhou
 Conditional Probability, Probability theory, Bullion coin, Gold coin

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