Final Answer:
1. Expected value provides the average outcome of a probability distribution.
2. EV = Σ (Probability of each outcome * Value of each outcome)
3. The equation calculates the sum of each possible outcome's value weighted by its probability.
4. EV = (1/2000) * ($15,000 - $10) = $7.50
Step-by-step explanation:
Expected value denoted as EV is a crucial concept in probability theory providing insight into the average outcome of a random event. In essence it quantifies the long-term average value one can expect from repeated trials of the same event.
The formula EV = Σ (Probability * Value) encapsulates the probability weighted sum of potential outcomes. Each outcome's likelihood is considered and this weighted average helps individuals make informed decisions by anticipating average gains or losses.
In the given example of purchasing a $10 raffle ticket for a car valued at $15,000 the EV is computed as (1/2000) * ($15,000 - $10) resulting in an expected gain of $7.50. This means that on average for every ticket purchased you can expect to gain $7.50.
Understanding EV is paramount in decision making as it provides a rational basis for evaluating risks and rewards. Whether applied in gambling finance or decision analysis, grasping expected value enhances one ability to navigate uncertain scenarios with more informed choices.