What is the expected profit? ​(Round to the nearest dollar as​ needed.)

Question

A man buys a racehorse for ​$20,000 and enters it in two races. He plans to sell the horse​ afterward, hoping to make a profit. If the horse wins both​ races, its value will jump to $60,000. If it wins one of the​ races, it will be worth $40,000. If it loses both​ races, it will be worth only ​$15,000. The man believes there is a 20​% chance that the horse will win the first race and a 40​% chance that it will win the second one. Assuming that the two races are independent​ events, find the​ man's expected profit.

Answer 1

Make a table of expectations (cost = 20000)

W both WR1 LR2 WR2 LR1 L both

Horse Price 60000 40000 40000 15000

Probability .2*.4=.08 .2*.6=.12 .4*.8=.32 .6*.8=.48 (note sumof row is 1.0)

Expectation 4800 4800 12800 7200 (this row sum is return)

P = Return - Cost

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