Question

The following game is played in a casino. The participant would roll two fair dice and if they sum to 8 or higher, the participant wins 4$ otherwise they lose 3$. What is the expected payout the casino will make as each game is played?

Answer #1

sum of the dice | list of outcomes favourable to sum | number of outcomes favourable to sum |

2 | (1,1) | 1 |

3 | (1,2),(2,1) | 2 |

4 | (1,3),(2,2),(3,1) | 3 |

5 | (1,4)(2,3),(3,2),(4,1) | 4 |

6 | (1,5),(2,4),(3,3),(4,2),(5,1) | 5 |

7 | (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) | 6 |

8 | (2,6),(3,5),(4,4),(5,3),(6,2) | 5 |

9 | (3,6),(4,5),(5,4),(6,3) | 4 |

10 | (4,6),(5,5),(6,4) | 3 |

11 | (5,6),(6,5) | 2 |

12 | (6,6) | 1 |

number of case in which participant wins $4=5+4+3+2+1=15

number of case in which participant lose $ 3=21

probability distribution table

X | 4 | -3 |

P(X) | 15/36=5/12 | 21/36=7/12 |

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