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Conditional Probability

Three purses ...

Question

Three purses contain respectively $(2 s i l v e r, 4 c o p p e r), (4 s i l v e r, 2 c o p p e r)$ and $(5 s i l v e r, 1 c o p p e r)$ coins. One of the purses is selected at random and then a coin is draw from it at random.If the coin draw is an copper coin, What is the probability that it is from the third purce?

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Solution

$U s i n g B a y e^{'} s R u l e, S e l e c t i o n o f e a c h b a g i s e q u a l l y l i k e l y w i t h p r o b a b i l i t y 1 / 3 P r o b a b i l i t y t h a t i t s c o m i n g f r o m t h e t h i r d b a g g i v e n i t s c o p p e r = \frac{P r o b a b i l i t y t h a t i t s c o m i n g f r o m t h e t h i r d b a g g i v e n i t s c o p p e r}{P r o b a b i l i t y t h a t t h e c o i n i s c o p p e r f r o m a n y b a g} = \frac{(1 / 3) \times (1 / 6)}{(1 / 3) \times (4 / 6) + (1 / 3) \times (2 / 6) + (1 / 3) \times (1 / 6)} = \frac{1}{7} = 1 / 7$

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