A player A plays a game against a machine At each round he

Last updated: 6/20/2023

A player A plays a game against a machine At each round he deposits one rupee in a slot and then flips a coin which has a probability p of showing a head If a head shows he gets back the rupee he deposited and one more rupee from the machine If a tail shows he loses his rupee Let A starts with 10 rupees and q 1 p 7 8 9 The probability that he is left with no money by the tenth round or earlier is a glo b d 10 r l a q10 1 10 pq 45p q b q 4 p q 36pq 7 c q 3pq 3 3p q p d g 0 1 10 pq 65p q 10 q 10 C p q10 r c pq The probability that all his money will be finished exactly at the twelfth round is 1 plo a q 2 b 1 pl c C pq d 12C p q The probability that he is left with no money by the 14th round or earlier is