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).

result dice A probability
$$1$$ ?
$$2$$ ?
$$3$$ $$1/6$$
$$4$$ ?
$$5$$ ?
$$6$$ 0
result dice B probability
$$1$$ ?
$$2$$ ?
$$3$$ $$1/6$$
$$4$$ ?
$$5$$ ?
$$6$$ ?
See development and solution

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
$$1$$ $$1/6$$
$$2$$ $$2/6$$
$$3$$ $$1/6$$
$$4$$ $$1/6$$
$$5$$ $$0$$
$$6$$ $$1/6$$
Hide solution and development
View theory