Finite Math-Probability Question?

or each of the following situations, give the number of outcomes in the sample space.

(a) Cal and Mark share an apartment. A list is made showing who is supposed to wash dishes for each day from Monday through Friday.

number of possible outcomes =

(b) Tom, Ed, Ann, Sue, and Peg make a list that shows each person's name and the day of the week the person was born (Monday, Tuesday, etc.). (Don't worry about the order in which the names are listed.)

number of possible outcomes =

(c) A tennis match is played where the winner must win 3 sets to win the match. (Think of the outcomes in terms of a tree diagram.)

number of possible outcomes =

1 Answer

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  • 4 years ago
    Best Answer

    (a) The list covers 5 days, and for each day there are 2 possible choices.

    2^5 = 32 possible lists

    [This includes lists in which the same person washes dishes each day. No on said the list had to be fair.]

    (b) We have 5 people, and each one could be born on any of 7 days of the week.

    7^5 = 1,6807

    (c) Let's call the players A and B, and list the winner of each set. For clarity, I'll write the tree left to right, set by set, with the cumulative list of set winners at each node.

    . . . . . .AAA (A wins)

    . . . . . .|

    . . AA--+

    . . .| . . |

    . . .| . . | . . . ..AABA (A wins)

    . . .| . . | . . . ..|

    . . .| . . AAB--+

    . . .| . . . . . . . |

    . . .| . . . . . . . | . . . . . AABBA (A wins)

    . . .| . . . . . . . | . . . . . |

    . . .| . . . . . . . AABB--+

    . . .| . . . . . . . . . . . . . |

    . . .| . . . . . . . . . . . . . AABBB (B wins)

    . . .|

    A--+

    | . .|

    | . .| . . . . . . . ABAA (A wins)

    | . .| . . . . . . . |

    | . .| . . .ABA--+

    | . .| . . .| . . . .|

    | . .| . . .| . . . .| . . . . . ABABA (A wins)

    | . .| . . .| . . . .| . . . . . |

    | . .| . . .| . . . .ABAB--+

    | . .| . . .| . . . . . . . . . .|

    | . .| . . .| . . . . . . . . . .ABABB (B wins)

    | . .| . . .|

    | . .AB--+

    | . . . . . |

    | . . . . . | . . . . . . . . . . ABBAA (A wins)

    | . . . . . | . . . . . . . . . ..|

    | . . . . . | . . . ..ABBA--+

    | . . . . . | . . . ..| . . . . . |

    | . . . . . | . . . ..| . . . . . ABBAB (B wins)

    | . . . . . | . . . ..|

    | . . . . . ABB--+

    | . . . . . . . . . . |

    | . . . . . . . . . . ABBB (B wins)

    |

    Start of play

    |

    | . . . . . . . . . .BAAA (A wins)

    | . . . . . . . . . .|

    | . . . . . BAA--+

    | . . . . . | . . . .|

    | . . . . . | . . . .| . . . . . BAABA (A wins)

    | . . . . . | . . . .| . . . . . |

    | . . . . . | . . . .BAAB--+

    | . . . . . | . . . . . . . . . .|

    | . . . . . | . . . . . . . . . .BAABB (B wins)

    | . . . . . |

    | . .BA--+

    | . .| . . .|

    | . .| . . .| . . . . . . . . . ..BABAA (A wins)

    | . .| . . .| . . . . . . . . . ..|

    | . .| . . .| . . . ..BABA--+

    | . .| . . .| . . . ..| . . . . . |

    | . .| . . .| . . . ..| . . . . . BABAB (B wins)

    | . .| . . .| . . . ..|

    | . .| . . .BAB--+

    | . .| . . . . . . . .|

    | . .| . . . . . . . .BABB (B wins)

    | . .|

    B--+

    . . .|

    . . .| . . . . . . . . . . . . ..BBAAA (A wins)

    . . .| . . . . . . . . . . . . ..|

    . . .| . . . . . . . BBAA--+

    . . .| . . . . . . . | . . . . . |

    . . .| . . . . . . . | . . . . . BBAAB (B wins)

    . . .| . . . . . . . |

    . . .| . . .BBA--+

    . . .| . . .| . . . .|

    . . .| . . .| . . . .BBAB (B wins)

    . . .| . . .|

    . . .BB--+

    . . . . . . |

    . . . . . . BBB (B wins)

    As you can see on the tree, we have 20 possible outcomes:

    AAA

    AABA

    AABBA

    AABBB

    ABAA

    ABABA

    ABABB

    ABBAA

    ABBAB

    ABBB

    BAAA

    BAABA

    BAABB

    BABAA

    BABAB

    BABB

    BBAAA

    BBAAB

    BBAB

    BBB

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