Roulette is played at a table similar to the one in the figure shown below. 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 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(gor o),p(oor f12), p(c1 or c3), p(eand f12), p(eor f12),p(s12 and t12), and p(oor c2).
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