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February 16th, 2009, 09:14 PM   #1
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Roulette Probability HELP!

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In the game Roulette, a ball spins on a circular wheel that is divided into 38 arcs of equal length, numbered 00, 0, 1, 2, ... , 35, 36. The number on the arc on which the ball stops is the outcome of one play of the game. The numbers are also colored as follows:
1, 3, 5, 7, 9, 12, 14, 16, 18, 19, 21, 23, 25, 27, 30, 32, 34, 36 are red,
2, 4, 6, 8, 10, 11, 13, 15, 17, 20, 22, 24, 26, 28, 29, 31, 33, 35 are black,
0, 00 are green.

Define the following events:
A: { Outcome is an even number (0 and 00 are considered neither odd nor even)
B: { Outcome is a red number }
C: { Outcome is a green number }
D: { Outcome is a low number 1-18
Find the following probabilities:
(a) P(D) = 18/ 38
(b) P(A U B) =
(c) P(A n B n C) =


I figured out A) because there is a total sample space of 38 and there are 18 numbers between 18-1. For B) I keep getting the wrong answer. First I would think that the outcome being and even number would make A be 18/36 and B 18/36 since there are only 18 reds and there are 18 even numbers. But that's how far I get and then I have no idea what the answer would be. C) I am entirely confused. would you make a Venn Diagram to find the intersection of A,B, and C?

Any input is appreciated.

Thanks
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Since the total number of possibilities is 38, you just need the number of possibilities in each questions divided by 38.
For (b) you add up the number of reds and the number of evens and subtract out those which are both (since they are being counted twice). I get 24.
For (c) there are 0 possibilities - being green means not red, not black, not even, not odd.
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February 18th, 2009, 01:56 PM   #2
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For (b), it helps to be able to count. Of the 18 reds, 8 are even, and 18 + 18 - 8 = 28. As far as I know, no version of roulette lets you put a single roulette token on the line between Red and Even in order to bet on both, but you can put one token (or more) on each.
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