Question

Craps is a dice game in which the players make wagers on the outcome of the roll, or a series of rolls, of a pair of dice. Most outcomes depend on the sum of the up faces of two, fair, six-sided dice.

A) Describe the sample space for all possible outcomes of rolling two dice. How many ways are there to roll a 5?

**b)**Determine all possible random variable values
and the probability of those outcomes. Find the probability of
rolling an 8. (Round to the nearest ten-thousandth.)

c)Construct a probability histogram (a relative frequency histogram of probabilities). What is the lower class boundary of the "6" class?

Answer #1

a) Sample space, S={ (1,1) (1,2) (1,3) (1,4) (1,5) (1,6) (2,1) (2,2) (2,3) (2,4) (2,5) (2,6) (3,1) (3,2) (3,3) (3,4) (3,5) (3,6) (4,1) (4,2) (4,3) (4,4) (4,5) (4,6) (5,1) (5,2) (5,3) (5,4) (5,5) (5,6) (6,1) (6,2) (6,3) (6,4) (6,5) (6,6) }

Number of ways to roll a 5 is 4.

S5 = { (1,4) (2,3) (3,2) (4,1) }

b) Let x denote random variable and P(x) denote the probability values. Here x is the sum of numbers obtained on rolling 2-dice.

x |
P(x) |

2 | 1/36 |

3 | 2/36 |

4 | 3/36 |

5 | 4/36 |

6 | 5/36 |

7 | 6/36 |

8 | 5/36 |

9 | 4/36 |

10 | 3/36 |

11 | 2/36 |

12 | 1/36 |

Probability of rolling an 8 =5/36 = **0.1389**

c) Probability histogram

Lower class boundary of 6 class is 0.

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