# Probability of investment loss/gain problem

I'm trying to determine the total expected gain or loss over a one year period given an investment that has the following probabilities (over the same one year period):

$P($2000 loss) = .25

$P($1000 profit) = .2

$P($5000 profit) = .15

$P($0 profit) = .4

My approach is as follows:

$P($loss) = .25(-2000) = - 500

$P($gain) = .2(1000)+.15(5000)+.4(0) = 950

Expected gain/loss = gain - loss

Expected gain/loss = 950 - 500 = $450 I feel like i'm missing something critical here, mostly pertaining to the 40% probability of breaking even. • What is the result of$0.2(1000)+.15(5000)+.4(0)$? Please calculate it again. – callculus Oct 31 '15 at 18:31 •$-2000\cdot0.25+1000\cdot0.2+5000\cdot0.15+0\cdot0.4=450$– barak manos Oct 31 '15 at 18:33 ## 1 Answer The best way to formulate this : Let$X$be a random variable with$P(X = -2000) = 0.25P(X=1000) = 0.2P(X = 5000) = 0.15P(X = 0) = 0.4$Then,$E(X)=(-2000)\times 0.25+1000\times0.2 +5000\times 0.15+0\times 0.4=450\$

• Thanks Peter, this is a much more clear and concise way to look at the problem. – JTW Oct 31 '15 at 18:37