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June 20th, 2013, 04:40 AM  #1 
Member Joined: Apr 2013 Posts: 35 Thanks: 0  Probability Question
There is a deck of cards where each card has symbols on it. The symbol may either be an oval, a rhombus, or a rectangle. The symbol may be one of three colors, red, green ,or purple. The symbol may be shaded with vertical lines, solid, or empty. There may be one, two, or three symbols on a card(all congruent). A set is a group of three cards that satisfy conditions. The conditions are that all three cards must have the same color, or all three have a different color; and likewise with each other attribute. The question is what is the probability of a set being present in 12 cards. This is how I solved it: I said there was 81 cards because 3^4=81. I also said there was 256 possible sets in those 81 cards because 4^4=256 I said there was 511920 possible grouping of three cards in the 81 cards because 81*80*79= 511920 I deduced the possibility of a group of three cards being a set was 0.05000781% which is 256/511920 There is also 1320 groups of three cards in 12 cards. 10*11*12 1320*0.0005000781=0.6601 or a 66% chance of a set being present. The correct answer is supposed to be 3% 
June 20th, 2013, 10:34 AM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,344 Thanks: 1024  Re: Probability Question
Jake, I got out of there midway through 1st paragraph...got no tylenols... 

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