Double Gamble

Discrete Mathematics Level 2

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 pick up one ball from each box with both hands simultaneously.

If you get the 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, for the red ball draw from the right box will cost you 7 dollars while the blue draw will earn you 8 dollars.

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


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