One thousand tickets ae sold at $1 each for a grand prize of $500.00. What is the expected value if a person purchases a single ticket?
To calculate the expected value, we need to determine the probability of winning and losing, as well as the corresponding values of each outcome.
In this scenario, there is only one grand prize of $500.00, and a total of 1,000 tickets are sold at $1 each. This means that the probability of winning the grand prize is 1/1,000 and the probability of losing is 999/1,000.
Next, we assign the corresponding values to each outcome. If you win, you receive $500.00, and if you lose, you receive nothing.
To calculate the expected value, we multiply the value of each outcome by its probability and sum them up:
(Expected Value) = (Probability of Winning) × (Value of Winning) + (Probability of Losing) × (Value of Losing)
Expected Value = (1/1,000) × ($500.00) + (999/1,000) × ($0.00)
Simplifying the equation, we get:
Expected Value = $500.00/1,000 + $0.00
Thus, the expected value of purchasing a single ticket is $0.50.
Please note that the expected value of $0.50 indicates the average outcome over a large number of trials. In any given trial, you could either win $500.00 or lose $1.00.