A man buys a racehorse for 20,000 and enters it in two...

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.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Probability

Probability quantifies the likelihood of the occurrence of specific events. It allows us to assign numerical values, typically between 0 and 1 or as percentages, to uncertain events, facilitating risk assessment and decision making in various contexts.

Expected Value

Expected value is the weighted average of all possible outcomes in a scenario, taking into account both the values of the outcomes and their probabilities. It is a central concept in probability theory and statistics used to predict the mean result of a random event over the long run.

Independence

Independence refers to the property of events being unaffected by the occurrence of other events. In probability, when events are independent, the probability of both happening is the product of their individual probabilities, which simplifies the computation of joint probabilities.

Profit Calculation

Profit calculation involves determining the difference between the final value or revenue from an investment and its initial cost. In situations involving uncertainty, such as probabilistic outcomes, the expected profit is derived by taking the expected value of the final outcomes and subtracting the initial investment.

Transcript

Please give Ace some feedback