Question: Two coins are flipped. You win $2 if either 2 heads or 2 tails turn up: you lose $3 if a head and a tail

Two coins are flipped. You win $2 if either 2 heads or 2 tails turn up: you lose $3 if a head and a tail turn up.

(a) What is the expected value of the game?

(b) For the game to be fair, how much should you lose if a head and a tail turn up?

Please show appropriate steps so I can fully understand how this problem is solved.

Thank you!

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