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Double Gamble

As shown above, the left box contains 1 red ball and 2 blue balls while the right box contains 2 blue balls and 3 red balls.

In a lucky draw game, you have to randomly and simultaneously pick up one ball from each box using both hands.

If you get a blue ball from the left box, you'll be rewarded 4 dollars, but you'll lose 5 dollars for the red draw. On the other hand, a red ball drawn from the right box will cost you 7 dollars while a blue draw will earn you 8 dollars.

What is the expected value of the bet earned from this game?


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