If a player makes a \(\$ 10\) bet on first dozen, they win \(\$ 20\) if one of the numbers \(1-12\) comes up but lose \(\$ 10\) otherwise. What is the expected value of this bet?

The following are about the casino game roulette. In this game, the dealer spins a marble around a wheel that contains 38 pockets that the marble can fall into. Each pocket has a number (each whole number from 0 to 36 , along with a "double zero") and a color ( 0 and 00 are both green; the other 36 numbers are evenly divided between black and red). Players make bets on which number (or groups of numbers) they think the marble will land on. The figure shows the layout of the numbers and colors, as well as some of the bets that can be made.

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0 00 1 2 3 4 5 6 789 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 1st Dozen 2nd Dozen 3rd Dozen 1 to 18 EVEN ODD 19 to 36 25 26 27 28 29 30 31 32 33 35 36 34 2 to 12 to 12 to 1