# 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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