Question

Q10. In each game, 2 unbiased normal 6-sided dice are tossed. If none of the dice shows a score of "1" and the total score of the two dice is more than 6, Robert wins $200; otherwise he loses $200. Robert starts the series of games with $2000, with the hope of reaching $3000 at which point he stops playing. However, if he loses all his money before this, the game also ends. Write out the values of each of the usual parameters in this gambler's ruin problem; (ii Compute the probability that the game ends with Robert losing all his starting $20o

Hi, anyone can help me with this question? The answer for i) is p = 19/36, q = 17/36, j =10, a = 15. The answer for ii) is is 0.1729. I need a full working for this question.

Answer 1

Solution : Given data Robert Wins $200 >> Robert loses $200 He starts the series of games with $2000 - The hope of reaching $3000 - In each game a unbiased normal 6-Sided dice are tossed. - from the above condition we have winning chances is total score of the dice more than 6. none shows alí. 7-5 . . 8-5 9- 4 10-3 11-12 12-1 20 Probability of wiming Ima (P)=0.5556

Probability of losing (9)= 1-P 1 =15 5915 ca)-0.444 - I The probability that the game ends with robert losing all his starting $200 = P(1,1) or p (2,12) or p13,13) or plu, 14) on Pl5,15) 01 p(6,16) ---- . ["Cola)*(+)"]+(?, (9* (*)") + [19974)") + ('(54)"] + (17.(13)*%*)*6(194)*7 : 0.000817 +0.00143 +0.0020607 0.0020 to.003698 to 004125 = 0.018 The probability that the game losing is 0.018 ends with Robert