Find the expected value of the winnings for a single lottery ticket if the jackpot is $40 million. How much can you expect to wi

Question

2 years ago

14

n or lose if you buy 500 lottery tickets? Should you actually expect to win or lose this amount? Explain.

1 answer:

amm1812 · Answer 1 · 2023-03-16T19:05:27+03:00

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:

$EV = x_1*p_1 + x_2*p_2 + ... + x_n*p_n$

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:

$EV = \$ 40.000.000*(1/500) + \$ 0*(499/500) = \$ 80,000$

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: