need help with the process please 5. (evel 2) In the board game Monopoly, a play

Question

need help with the process please

5. (evel 2) In the board game Monopoly, a player who is in jail may get out by rolling doubles. the player does not roll doubles, then he or she is stuck in jail for another turn. However, if the player does not roll doubles by the end their third try, then be or she must pay $50 to get out of jail. Let X be the first roll on which a player rolls doubles. The PMF of X is given by px (a) where m 1,2,3,.... What is the probability that a player who is in jail will get out of jail before having to pay the $50 fine? Answer: 0.421296

Explanation / Answer

Probability that the person will roll doubles on the x-th turn, PX(X=x) = (5/6)x-1(1/6)

P(X=1) = (1/6)

P(X=2) = (5/6)*(1/6)

P(X=3) = (5/6)2(1/6)

Thus the requires probability = P(X=1) + P(X=2) + P(X=3)

                                                          = (1/6) + (5/6)*(1/6) +(5/6)2(1/6)

                                                         =0.4213

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