# Find the average price per gallon using Wald's Identity

The average price of gas is 1.85 per gallon. Assume that each week it goes up 5 cents with probability 40% or down 5 cents with probability 60%. Find the probability that the average price per gallon goes down to 1 before it comes back to 2.

I have the answer to this problem and I know this is a two sided asymmetric case with $a=20$, $b=40$, $p=.4$, and $q=.6$. What I do not understand is how $x=37$. Can someone explain how it comes out to that using Wald's Identity?

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$1.85/0.05 = 37$. So rather than thinking of the cost of gas being 1.85 and going up and down in 5-cent intervals, you can think of it as a simple random walk on the integers, starting at 37 and going up or down by one.