(Answered) Question suppose you start with 10 and repeatedly bet 2

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Question: Suppose you start with $10 and repeatedly bet $2 (instead of $1), having probability p of winning each time. Suppose your goal is $100, i.e., you keep on betting until you either lose all your money, or reach $100.

(a) As a function of p, what is the probability that you will reach $100 before losing all your money? Be sure to justify your solution. (Hint: You may find yourself dividing both 10 and 100 by 2.)

(b) Suppose p = 04. Compute a numerical value for the solution in part (a).

(c) Compare the probabilities in part (b) with the corresponding probabilities if you bet just $1 each time. Which is larger?

(d) Repeat part (b) for the case where you bet $10 each time. Does the probability of success increase or decrease.

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