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

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