Calculating Expected Value for Sweepstakes Prizes: A Guide

In summary: So in summary, the prizes and chances of winning for this sweepstakes are listed as: $5900 (probability of 1/8100), $2500 (probability of 1/6200), $600 (probability of 1/4700), and $300 (probability of 1/2600). To find the expected value of the amount won for one entry costing 75 cents, use the formula E[X] = sum of (X_i * P(X_i)), with X_i being the amount of each winning and P(X_i) being the corresponding probability. Don't forget to subtract the cost of entry from the total expected value. The final answer is $0.62.
  • #1
layzieb81
1
0
The prizes that can be won in a sweepstakes are listed below together with the chances of winning each one.

$5900(1 chance in 8100); $2500( 1 chance in 6200); $600 (1 chance in 4700); $300(1 chance in 2600)
Find the expected value of the amount won for one entry if the cost to enter is
75 cents.

Now I am having trouble setting this up as a probability distribution. I just don't know where to start or what goes where. I know the awnser is $0.62..but i just can't figure out the steps. So far i'v been doing it like this

x P(x)
----- ------
Win $5899.25 ?
Lose -$.75 ?

Well I think I'm setting up "x" wrong and I just don't know what the probability should be. So any help would be apreciated.
 
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  • #2
For example, 1 chance in 100 is a probability.
So you have the probability of every winning and the amount of each winning. Now, the expected value is

[tex]E\left[ X \right] = \sum\limits_{i = 1}^n {X_i P\left( {X_i } \right)}[/tex]

[tex]X_i[/tex] is the amount of each winning and [tex]P\left( {X_i } \right)[/tex] is the probability of each winning.
And don't forget to take into account the 75 cents the entry consts.
 
  • #3
"One chance in 8100" means the probability is 1/8100, "one change in 6200" mean the probability is 1/6200, etc.
 

What is expected value?

Expected value, also known as mean or average, is a statistical measure used to calculate the predicted value of a random variable. It is calculated by multiplying each possible outcome by its probability and then summing them all together.

Why is expected value important?

Expected value is important because it helps in decision-making by providing a numerical representation of the potential outcomes of a situation. It allows scientists to determine the most likely outcome and make informed choices based on that information.

How is expected value calculated?

The formula for calculating expected value is E(X) = Σ x * P(x), where E(X) is the expected value, x is the possible outcome, and P(x) is the probability of that outcome occurring. It is important to note that the sum of all probabilities must equal 1.

What are some real-life applications of expected value?

Expected value is used in various fields, including finance, gambling, and insurance. For example, in finance, it is used to evaluate investments and determine the potential returns. In gambling, it helps players decide which bets offer the highest expected value. In insurance, it is used to calculate premiums based on the expected losses.

How does expected value relate to risk?

Expected value is often used in conjunction with risk analysis to assess the potential risks and rewards of a decision. A higher expected value indicates a greater potential reward, but it does not account for the level of risk involved. Scientists must consider both expected value and risk when making decisions.

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