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You are deciding whether or not to enter a lottery. An entry ticket costs 50 cents. If you play, you either win exactly one of the prizes or nothing. The prize amounts and the chances of winning them are as follows:

$25 million: one chance in 200 million

$150000: one chance in 150 million

$75000: one chance in 30 million

$15000: one chance in a million

$500: one chance in 800000

$70: one chance in 6000

What is the expected value of the amount of money you will make if you enter the lottery, taking into account the price of the ticket? Enter your answer as a decimal and make sure that at least 10 digits after the decimal point are correct.

I thought I knew how to do this. I calculated the expected value by $\dfrac1{6000} \times (70-.5))$ for the $70 prize, and so forth multiplying the probability minus the value of .5 and adding all the quantities. However, this didn't equal the right answer. So where am I going wrong?

Rodrigo de Azevedo
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Jilly
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1 Answers1

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What about adding also $(1-[\text{sum of all other probabilities}])\times(0-\mathord.5)$? In this case, you win nothing, just spend $50$ cents.

triple_sec
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  • ah thank you, i was thinking about that but i kept doing the expected value of complement of each probability * -.5 so the answer wasn't making sense. Thanks! – Jilly Feb 01 '14 at 03:10
  • An alternative would be to add up the values $\text{prize } \times \text{ probability}$ to give the expected gross winnings, and only then subtract the ticket price $$0.50$ from the total to give the expected net winnings. – Henry Jul 01 '16 at 10:48