Write 15 cookies to 40 brownies
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We want to find the expected value of the given game, and then analyze it.
We will see that the expected value of the game is $80,000
And you can expect to win this amount.
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For a game with outcomes {x₁, x₂, ..., xₙ}, each one with probability {p₁, p₂, ..., pₙ}, the expected value is given by:
In this particular case, we have two outcomes:
x₁ = winning $40 million.
x₂ = not winning.
Because there are 500 tickets and you have one of them (and there is only one winning ticket) the probability of winning will be:
p₁ = 1/500
While the probability of not winning is given by all the tickets that you do not have:
p₂ = 499/500
Then the expected value is:
So the expected value is really large.
Now, answering the final question:
Should you actually expect to win or lose this amount?
This is a positive expected value, meaning that you must expect to win it.
If you want to learn more, you can read: