A gambler enters a casino with $5. He will play until he has at least $10 or $0,

Question

A gambler enters a casino with $5. He will play until he has at least $10 or $0, whichever comes first. Each bet will lose $1 with a probability of 0.75, win $1 with a probability of 0.2, and win $2 with a probability of 0.05.

a) What proportion of the time will the gambler end up with $10, and what proportion of the time will the gambler end up with $0?

b) If the gambler starts with $9, what proportion of the time will the gambler end up with $10, and what proportion of the time will the gambler end up with $0?

Please show all work and process

Explanation / Answer

a) In the second time will the gambler end up with $10

The proportion is

0.05*0.05*0.2= 0.0005

In the five time will the gambler end up with $0

The proportion is 0.1680

b) The proportion of the time will the gambler end up with $10 is 0.2

The proportion of the time will the gambler end up with $0 is 0.75^9=0.0403

Time 1 4 6 7 Time 2 3 5 6 7 8 9 Time 3 2 4 5 6 7 8 9 10 Time 4 1 3 4 5 6 7 8 9 10 Time 5 0 2 3 4 5 6 7 8 9 10

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