at a casino, a coin toss game works as follows. Quarters are tossed onto a checker-board. the gaming dealer keeps all the quarters, but for

Question

at a casino, a coin toss game works as follows. Quarters are tossed onto a checker-board. the gaming dealer keeps all the quarters, but for each quarter landing entirely within one square of the checkerboard the gaming dealer pays a dollar. Assume that the edge of each square is twice the diameter of a squatter, and that the outcomes are described by coordinates chosen at random. Is this a fair game

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Reagan 4 months 2021-10-08T13:50:39+00:00 1 Answer 0 views 0

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    2021-10-08T13:52:31+00:00

    Answer:

    Step-by-step explanation:

    According to the data given ;

    • edge of square = 2 x diameter of a quarter
    • let diameter of a quarter = d
    • area of quarter = πd²/4
    • Area of each square = (2d)² = 4d²
    • Thus the probability of a quarter completely within a square = πd²/4/4d² = 0.`196

    Now if one losses a quarter or gains a dollar, Probability of earning a dollar = 4 x 0.196 = 0.784

    • As such, since probability of winning is more than 0.5, it is a fair game.
    • It should be noted that Probability of winning + probability of loosing = 1
    • Hence probability of loosing = 1 – 0.784 = 0.804

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