Aman buys a racehorse for $20,000 and enters it in two races. He plans to sell t

Question

Aman 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 $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. Can you explain to me in DETAIL how to get the probabilities for each of the races won? There are "step by step solutions" here, but I still don't get it...I need more details to understand.

Explanation / Answer

Cost of the Horse = $ 20,000

The Probability matrix of the outcomes of the two Races are -

To calculate the the Expected Profit we will have to calculate the Expected Value of the Horse from different Outcomes that can be be expected with the two Races. Then we will deduct the Cost from the Expected Value.

The Expected Value of the Horse from all the different options will be the Value of the horse multiplied by the probability of these outcomes.

The Probabilities for the Outcomes is the probability of Race 1 AND Race 2. This probability is calculated by the Probability of Race 1 multipled by Probability of Race 2.

Prob

(Race1)

Prob

(Race2)

Expected Value of the Horse = Expected Value (Outcome 1) + Expected Value (Outcome 2) + Expected Value (Outcome 3) + Expected Value (Outcome 4)

Expected Value of Horse = 6,000 + 7,000 + 12,000 + 5,600 =  30,600

less Cost of Horse = (20,000)

Expected Profit = 10,600

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