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Question is :
Consider 21 locations, numbered with integers from -10 to 10, and lined up in the order
−10, −9, . . . , −1,0,1, . . . ,9,10, from left to right. Suppose that a person starts at location 0, ﬂips a fair coin, and moves one spot to the right if the result is Heads or moves one spot to the left if the result is Tails. If he keeps ﬂipping the coin and moving one spot to the right or left based on each outcome, what is the probability that he either reaches location 10 or location -10 before he returns to location 0? (Hint: Make use of one of the “gambler’s ruin” results given on pp. 84-85 of the text, being sure to note that the case of p = 1/2 is treated diﬀerently from the case of p 6= 1/2. You may or may not have to modify the result to be able to apply it to the situation being considered here.) Be sure to give some sort of explanation for your answer, but there is no need to present a derivation already given in the book.