Question

Racehorse A man buys a racehorse for $20,000 and en- ters 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 $100,000. If it wins one of the races, it will be worth $50,000. If it loses both races, it will be worth only $10,000. The man believes there’s a 20% chance that the horse will win the first race and a 30% chance it will win the second one. Assuming that the two races are independent events, find the man’s expected profit.

Answer 1

Answer: $10,600

Step-by-step explanation:

Worth raises to $100,000 by winning both races

Worth raises to $50,000 by winning one race

Worth decreases to $10,000 by loosing both

Probabilty of winning both races=$0.2\times 0.3$

Probabilty of winning one race=$0.2\times 0.7+0.8\times 0.3$=0.38

Probabilty of loosing both races=$0.8\times 0.7$=0.56

Expected profit=$0.06\left ( 100,000-20,000\right )+0.38\left ( 50,000-20,000\right )+0.56\left ( 10,000-20,000\right )$

=$10,600