Roulette is played at a table similar to the one in Figure 5.36. A wheel with the numbers 1 through 36 ( evenly distributed with the colors red and black) and two green numbers 0 and 00 rotates in a shallow bowl with a curved wall. A small ball is spun on the inside of the wall and drops into a pocket corresponding to one of the numbers. Players may make 11 different types of bets by placing chips on different areas of , what is the probability that the outcome will be green twice in a row? What is the probability that the out-come will be black twice in a row?

the table. These include bets on a single number, two adjacent numbers, a row of three numbers, a block of four numbers, two adjacent rows of six numbers, and the five number combinations of 0, 00, 1, 2, and 3; bets on the numbers 1– 18 or 19– 36; the first, second, or third group of 12 numbers; a column of 12 numbers; even or odd; and red or black. Payoffs differ by bet. For instance, a single number bet pays 35 to 1 if it wins; a three- number bet pays 11 to 1; a column bet pays 2 to 1; and a color bet pays even money. Define the following events: C1 = column 1 number, C2 = column 2 number, C3 = column 3 number, O = odd number, E = even number, G = green number, F12 = first 12 numbers, S12 = second 12 numbers, and T12 = third 12 numbers. a. Find the probability of each of these events. b. Find P(G or O), P(O or F12), P(C1 or C3), P(E and F12), P(E or F12), P(S12 and T12), P(O or C2).

a. Find the probability of each of these events.

b. Find P(G or O), P(O or F12), P(C1 or C3), P(E and F12), P(E or F12), P(S12 and T12), P(O or C2).

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1st 12 2nd 12 3rd 12 1 to 18 EVEN RED BLACK | ODD | 19 TO 36