Question

One thousand tickets are sold at $3 each. One ticket will be randomly selected and the winner will receive a color television valued at $358. What is the expected value for a person that buys one ticket?

Answer 1

The expected value for a person buying one ticket in a raffle with one thousand tickets sold at $3 each for a $358 television is approximately -$2.639, indicating an average loss of this amount.

Step-by-step explanation:

In a raffle where one thousand tickets are sold at $3 each and one winning ticket will be drawn to win a color television worth $358, we can calculate the expected value for a person buying one ticket. The concept of expected value provides a way to predict the average outcome of a random event that can happen multiple times, such as a raffle.

To find the expected value, we use the formula:

E(X) = (probability of winning) × (value of the prize) - (probability of losing) × (cost of the ticket)

Here's the step-by-step calculation:

1. The probability of winning the television is 1/1000, since there is only one winner.
2. The value of the price is $358.
3. The probability of not winning is 999/1000, because there are 999 ways to lose.
4. Each ticket costs $3.
5. The expected value is calculated as follows:
6. E(X) = (1/1000) × $358 - (999/1000) × $3
7. When you work out the math:E(X) = $0.358 - $2.997 = -$2.639

The expected value of buying one ticket is approximately -$2.639. This means that, on average, a person can expect to lose about $2.639 when they buy one ticket for the raffle.