An oil exploration firm is to drill $10$ wells, with each well having probability $0.1$ of successfully producing oil.
It costs the firm ${10}$ million dollars to drill each well.
A successful well will bring in oil worth $500$ million dollars.
Calculate the firm's expected gain from the $10$ wells. (Answer: $580$ million dollars).
My try:
I thought it was a binomial distribution.
Let $X$ denote the number of wells that successfully produce oil.
Let $Y$ denote the firm's gain from the $10$ wells.
$E[X] = 10(0.1) = 1$
$Y = 500,000,000X - 10,000,000(10) = 500,000,000X - 100,000,000$
$E[Y] = 500,000,000E[X] - 100,000,000 = 500,000,000(1) - 100,000,000 = 400,000,000 $ dollars
I don't know how they got $580,000,000$