Imagine that you are doing research for a term paper in your English class and you have chosen the topic of “expected winnings of a lottery.” You find the following information for your state’s lottery:
Prize Probability
Jackpot 1 in 60,000,000
$12,000 1 in 100,000
$750 1 in 10,000
$5 1 in 200
You know that it costs $2 to purchase the lottery ticket in order to play the game. What would you conclude in your term paper regarding the calculated expected value of your state’s game if the jackpot is $50,000,000? How would you interpret the meaning of this expected value so that the reader of your paper would understand it well?
To calculate the expected value of a lottery game, you need to multiply the probability of winning each prize by the amount you would win for that prize, and then add up all of those values. In this case, you have the following information:
Prize Probability
Jackpot 1 in 60,000,000
$12,000 1 in 100,000
$750 1 in 10,000
$5 1 in 200
Given that the jackpot is $50,000,000, we can calculate the expected value by multiplying each prize amount by its respective probability and adding up the values:
Expected Value = (Probability of Jackpot x Jackpot Amount) + (Probability of $12,000 x $12,000) + (Probability of $750 x $750) + (Probability of $5 x $5)
Expected Value = (1/60,000,000 x $50,000,000) + (1/100,000 x $12,000) + (1/10,000 x $750) + (1/200 x $5)
Calculating this expression will give us the expected value of playing the lottery.
Now, let's interpret the meaning of the expected value for the reader to understand it well:
The expected value of a lottery game represents the average amount a player can expect to win per ticket, based on the probabilities and prize amounts. In this case, if the jackpot is $50,000,000, the calculated expected value will provide an indication of whether the game is expected to be a favorable or unfavorable choice.
If the expected value is positive, it means that, on average, a player would win more money than they spend, suggesting the game may offer potential profits. Conversely, if the expected value is negative, it means that, on average, a player would lose more money than they spend, indicating the game is likely not a good investment.
Therefore, in your term paper, after calculating the expected value, you would conclude whether the state's lottery game is expected to be a profitable endeavor or not, based on the calculated value.