# Problems from The probability function

The owner of a casino fakes two dices so that in dice $$A$$ we can never get a $$6$$ (and get twice as many ones), and in dice $$B$$ we never get a $$5$$ (and twice as many twos).

• Fill in the following table of probabilities for every dice:
 result dice A probability $$1$$ ? $$2$$ ? $$3$$ $$1/6$$ $$4$$ ? $$5$$ ? $$6$$ 0
 result dice B probability $$1$$ ? $$2$$ ? $$3$$ $$1/6$$ $$4$$ ? $$5$$ ? $$6$$ ?
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### Development:

• The impossible events have zero probability $$(A=6, B=5)$$. As we are been told, there is twice the probability of observing events $$A=1$$ and $$B=2$$ (probability $$2/6$$):
 result dice A probability $$1$$ $$2/6$$ $$2$$ $$1/6$$ $$3$$ $$1/6$$ $$4$$ $$1/6$$ $$5$$ $$1/6$$ $$6$$ $$0$$
 result dice B probability $$1$$ $$1/6$$ $$2$$ $$2/6$$ $$3$$ $$1/6$$ $$4$$ $$1/6$$ $$5$$ $$0$$ $$6$$ $$1/6$$

### Solution:

 result dice A probability $$1$$ $$2/6$$ $$2$$ $$1/6$$ $$3$$ $$1/6$$ $$4$$ $$1/6$$ $$5$$ $$1/6$$ $$6$$ $$0$$
 result dice B probability $$1$$ $$1/6$$ $$2$$ $$2/6$$ $$3$$ $$1/6$$ $$4$$ $$1/6$$ $$5$$ $$0$$ $$6$$ $$1/6$$
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