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20 June, 13:29

3. What is the net amount that a contestant should expect to win per game if the game were to be played many

times?

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  1. 20 June, 16:28
    0
    0.55

    Missing Statement:

    At a carnival, one game costs $1 to play. The contestant gets one shot in an attempt to bust a balloon. Each balloon

    contains a slip of paper with one of the following messages:

    Sorry, you do not win, but you get your dollar back. (The contestant has not lost the $1 cost.) Congratulations, you win $2. (The contestant has won $1.) Congratulations, you win $5. (The contestant has won $4.) Congratulations, you win $10. (The contestant has won $9.)

    If the contestant does not bust a balloon, then the $1 cost is forfeited. The table below displays the probability

    distribution of the discrete random variable, or net winnings for this game

    Net Winnings - 1 0 1 4 9

    Probability 0.25? 0.3 0.08 0.02

    Step-by-step explanation:

    First we find of the missing probability for net winnings of 0, in which case:

    When you receive the message, "Sorry, you do not win, but you get your dollar back," then your net winnings is 0$.

    The probability of winning 0$ is = 1 - 0.25 - 0.3 - 0.08 - 0.02 = 0.35

    So now we have the complete details:

    Net Winnings - 1 0 1 4 9

    Probability 0.25 0.35 0.3 0.08 0.02

    Now we need to find, the net amount that a contestant should expect to win is the expected value of the probability distribution.

    Expected value of probability distribution = - 1 (0.25) + 0 (0.35) + 1 (0.3) + 4 (0.08) + 9 (0.02)

    Expected value of probability distribution = 0.55

    The net amount that a contestant should expect to win per game if the game were to be played many times is 0.55
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