Expected value question -- Probabilities when tossing two coins

[RM86Z]

Summary:: checking an expected error

Given the question:

"If a person tosses two coins and gets two heads, the person wins $10.
How much should the person pay if the game is to be fair?"

The book gives the answer as $2.5 while I calculate $3.333...

E(X) = 0 = $10(1/4) - a(3/4) => a = $(10/3)

This makes sense when we consider tossing the coins four times in a row we expect to win once and lose three times so winning $10 and losing 3 x $3.333 = $10.

[Moderator's note: moved from a technical forum.]

 

[FactChecker]

If this is a question about "pay-to-play", then he pays to play even when he ends up winning the $10. I think that will give their answer.

 

[RM86Z]

Yes that is true thank you very much!

 

[PeroK]

That said, if you win at the bookies you also get your stake back.

 

[jedishrfu]

But if you lose at the bookies you may need to buy a new shirt on loan of course. And then make sure you pay up before you’ll need new fingers And/or other appendages.