1. ## probability question

An investor owns shares in a stock whose present value is 25. she has decided that she must sell her stock if it goes either down to 10 or up to 40. If each change of price is either up 1 point with probability 0.55 or down 1 point with probability 0.45, and the successive changes are independent, what is the probability that the investor retires a winner?

The answer is (1-(9/11)^15)/(1-(9/11)^30), which means that we need to divide P(down one point) by P(up one point), but I don't understand the logic behind this answer.

2. ## Re: probability question

Break it down recursively. There will not be that many terms.

Let's define a notation. P(v) is the probability that starting at a value of v, she retires a winner.

P(11)=0.55P(12)
P(12)=0.55P(13)+0.45P(11)
P(13)=0.55P(14)+0.45P(12)
.
.
.
P(38)=0.55P(39)+0.45P(37)
P(39)=0.55+0.45P(38)