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 $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.

The expected profit is $10,600.

Step-by-step explanation:

The expected profit can be calculated as the sum of the possible outcomes weighted by their probability of occurrence.

In this case, there are four possible outcomes:

1) The horse win both races. The value of the horse will be $100k-$20k=$80k.

The probability of this outcome is:

2) The horse win the first race, but lose the second one. The value will be $50k-$20k=$30k.

The probability is:

3) The horse lose the first race, but win the second one. The value will be $50k-$20k=$30k.

The probability is:

4) The horse lose both races. The value will be $10k-$20k=-$10k.

The probability is:

Then, the expected profit can be calculated as: