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February 16th, 2009, 09:15 PM  #1 
Newbie Joined: Feb 2009 Posts: 2 Thanks: 0  Roulette Probability HELP!!
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 118 Find the following probablilities: (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 181. 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 
February 18th, 2009, 09:56 PM  #2 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: Roulette Probability HELP!!
Let X denote the number of members of X, so (for example) A = 18. A union B = A + B  A intersect B = 36  A intersect B. You need to subtract out the even red numbers  just count them, if nothing else. B intersect C = 0 since no wedges are both red and green. 

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