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Math Help - 4 sided die, rolled twice problem

  1. #1
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    4 sided die, rolled twice problem

    A four-sided die is rolled twice and the scores (1, 2, 3 or 4) recorded on each roll.
    (a) What is the sample space for this experiment?
    (b) Let X equal the larger of the two outcomes if they are different and the common value if they are the same. Write down the probability table for x.
    (c) Find a formula for the probability (mass) function, (p.m.f.), f(x).

    I know Part (A).

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

    I'm not sure of what there asking for Part (B). Would X be everywhere there is 3 and 4 both when its different [(3,4)?] and when they are same [(3,3) & (4,4)?]?

    Part (C) I'm not sure of also but I know it would be some formula including X and the denominator being 16.

    Thanks
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  2. #2
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    Re: 4 sided die, rolled twice problem

    Quote Originally Posted by Mizen View Post
    A four-sided die is rolled twice and the scores (1, 2, 3 or 4) recorded on each roll.
    (a) What is the sample space for this experiment?
    (b) Let X equal the larger of the two outcomes if they are different and the common value if they are the same. Write down the probability table for x.
    (c) Find a formula for the probability (mass) function, (p.m.f.), f(x).
    I know Part (A).
    S = {(1,1),(1,2),(1,3),(1,4),(2,1),(2,2),(2,3),(2,4),( 3,1),(3,2),(3,3),(3,4),(4,1),(4,2),(4,3),(4,4)}
    I'm not sure of what there asking for Part (B). Would X be everywhere there is 3 and 4 both when its different [(3,4)?] and when they are same [(3,3) & (4,4)?]?
    Part (C) I'm not sure of also but I know it would be some formula including X and the denominator being 16.
    X=1 in only one way, \{(1,1)\}.

    But X=4 happens in each of \{(1,4),(2,4),(3,4),(4,1),(4,2),(4,3),(4,4)\} or seven ways.
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