Justin buys a racehorse for $25,000 and enters it in two races. he plans to sell the horse afterwards, hoping to make a profit. if the horse wins both races, its value will jump to $100,000. if the horse wins one of the races, it will be worth $60,000. if it loses both races, it will be worth only $15,000. justin believes that there is a 25% chance the horse will win the first race and a 35% chance it will win the second race. assume the two races are independent of one another. what is the the expected value?

1) Justin wins the first race, but loses the second race = (0.25) (1-0.35) = 0.1625 
2) Justin loses the first race, but wins the second race = (1-0.25) (0.35) = 0.2625 
3) Justin wins both races = (0.25) (0.35) = 0.0875 
4) Justin loses both races = (1-0.25) (1-0.35) = 0.4875 

If you add up all four probabilities, you will note that it equals 1.0. This means we did the calculations correctly. 

Expected value = ($60,000) (0.1625) + ($60,000) (0.2625) + ($100,000) (0.0875) + ($15,000) (0.4875) 

Expected value = $41,562.50 (these are his expected winnings from the races) 

Expected Profit = $41,562.50 - $25,000 = $16,562.50