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Math Help - probability distribution of X

  1. #1
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    probability distribution of X

    so heres the question
    i dont know how to construct a probability distribution of X
    the answers are shown below but i dont know how they were obtained

    A player tosses a coin. If he obtains a head he is permitted to throw a die and receive, in dollars, the number of points showing on the die. If he obtains a tail he is not permitted to throw the die but he does receive $2. Let X be the number of dollars that a player can win in one attempt at this game if bith the coin and the die are fair. What is the probability distribution of X?


    X {1, 2, 3, 4, 5, 6}
    P(X) {0.083, 0.583, 0.083, 0.083, 0.083, 0.083}
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  2. #2
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    i finally got this question!

    when u toss a coin you have a 50/50 chance of getting a head or tail and if you get head you roll a die to get either 1, 2, 3, 4, 5, 6, BUT if you get a tail you simply get $2



    COIN --> (0.5 chance) Head --> 1, 2, 3, 4, 5, 6 --> $1, $2, $3, $4, $5, $6
    ~ 1/6 = 0.166 chance of getting either 1, 2, 3, 4, 5, 6,

    --> (0.5 chance) Tail --> $2


    so for X = $1, you get 0.166 x 0.5 chance of getting a head = 0.08333
    for X = 3, 4, 5, 6 it is the same 0.166 x 0.5 to get = 0.08333

    but for X = $2 you have (0.166x0.5) + 0.5 from tail = 0.5833
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