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Stephy7878 February 16th, 2009 08:15 PM

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 1-18
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 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

CRGreathouse February 18th, 2009 08:56 PM

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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