What is the expectation for the \(\$ 1\) bets in Problems 21-30 on a U.S. roulette wheel? See Figure 13.8

Twelve-number bet

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4 16 33 1 20 14 31 9 22 18 29 28 12 35 3 26 0 32 15 19 4 21 2 25: 4 21 2 25 17 34 6 27 13 36 113 EE 91 +29 00 01 82 8 Here is how bets are placed on the roulette table. 0 & 00 Split Pays 17 to 1 Single 0 or Double 00 Played the same as single number bets. Pays 35 to 1 Even Money Bets Black, Red, Even, Odd, 1 to 18, 19 to 36. Pays 1 to 1 Twelve Numbers or Section Bets Covers all 12 numbers in that section. Pays 2 to 1 0 to 00 Split Place bet here for convenience. Pays 17 to 1 Column Bets Covers each column of 12 numbers. Pays 2 to 1 1 TO 18 EVEN ODD 19 TO 36 1ST 12 2ND 12 3RD 12 00 2 3 4 5 6 78 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 2 TO 1 2 TO 1 2 TO 1 Five Numbers Covers 0, 00, 1, 2, 3, only. Pays 6 to 1 Single Number Play any straight up number, including 0 or 00. Pays 35 to 1 Two Numbers or Split Covers both numbers. Pays 17 to 1 Three Numbers Covers the three numbers across (example: 16, 17, 18). Pays 11 to 11 Four Numbers Covers four joining numbers. Pays 8 to 1 Six Numbers Covers six numbers across. Pays 5 to 1 FIGURE 13.8 U.S. roulette wheel and board