Explain the general expression for the probability


A game consists of tossing disks onto a table marked in squares of side a. If the disk does not touch any line or edge, the player wins. It is assumed that the player can at least hit the table. If r is the radius of the disk, what should the ratio r/a be if the game operator wants a player to have a chance less than p of winning. Let m(E) be a measure of set E⊂R^n , n dimensional realspace. Let Ω be an equiprobable sample space contained in R^n with finite measure. The general expression for the probability p that a point lies in a subset B⊆Ω is given by p=m(B)/m(Ω).

 

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Mechanical Engineering: Explain the general expression for the probability
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