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. Will Justin make a profit
To determine if Justin will make a profit, we need to calculate the expected value of the horse after the races.
The probability of the horse winning both races is given by: 0.25 * 0.35 = 0.0875
In this scenario, the value of the horse is $100,000.
The probability of the horse winning only one race is given by: (0.25 * 0.65) + (0.75 * 0.35) = 0.4875
In this scenario, the value of the horse is $60,000.
The probability of the horse losing both races is given by: 0.75 * 0.65 = 0.4875
In this scenario, the value of the horse is $15,000.
Now we can calculate the expected value of the horse:
Expected value = (0.0875 * $100,000) + (0.4875 * $60,000) + (0.4875 * $15,000)
Expected value = $8,750 + $29,250 + $7,312.50
Expected value = $45,312.50
Since the expected value of the horse is greater than the purchase price of $25,000, Justin is expected to make a profit.