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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

Respuesta :

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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