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June 18th, 2008, 07:43 AM  #1 
Newbie Joined: Jun 2008 Posts: 4 Thanks: 0  Probability in a Trading Card Game??
Hey everyone. I'm writing an article for a trading card game and I have a math problem that can be simplified this way:
If a pack is chosen at random, then a card is pulled from it at random, what is probability that: 1: the card is red and is labelled a certain number from 1 to 15? Answer: 1/8 * 1/15 = 1/120 2: the card is blue and is labelled a certain number from 1 to 53? Answer: 7/8 * 1/53 = 7/424 Now, how do I calculate that for the entire BOX (36 packs)? I think I would use (1/120)^36? Which equals a number I don't under stand (1.41083E75 ??). Or, do I say (1/120)*36 = 0.3? For the blue cards: (7/424) * 36 = .59 & (7/424)^36= 6.89221E65 ?? The number that spits out in the end, what unit is it? 0.3 of a what? or 1.41083E75 whats? I'd like to be able to say, "You have a 1 in ____ chance of opening a particular red card in a box of 36 packs." Thanks for your help!! Bye for now, Ray 
June 18th, 2008, 04:59 PM  #2  
Senior Member Joined: Oct 2007 From: Chicago Posts: 1,701 Thanks: 3  Re: Probability in a Trading Card Game?? Quote:
And by the way, 1.41... E75 means 1.41...* 10^(75) Quote:
Quote:
Quote:
 
June 18th, 2008, 05:18 PM  #3 
Newbie Joined: Jun 2008 Posts: 4 Thanks: 0  Re: Probability in a Trading Card Game??
AH! So both are right. My questions were mixed up! LOL Thanks for the help! I get it! 
June 30th, 2008, 12:49 PM  #4 
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: Probability in a Trading Card Game??
First of all, I'm not sure that the probabilities for the individual packs are uniform for a given box  usually cards are not so thoroughly randomized, so that a given box will always have at least one of the 15 red cards (say). But supposing that it is uniformly random: Chance of a particular red card in a pack: 1/120 Chance of not getting that particular red card: 119/120 Chance of not getting that particular red card in 36 packs: (119/120)^36 Chance of getting that particular red card in 36 packs: 1  (119/120)^36, or about 26%. Chance of a particular blue card in a pack: 7/424 Chance of not getting that particular blue card: 417/424 Chance of not getting that particular blue card in 36 packs: (417/424)^36 Chance of getting that particular blue card in 36 packs: 1  (417/424)^36, or about 45%. 1/120 * 36 = 0.3 is the expected number of each of the 15 red cards per box. 7/424 * 36 ~= 0.59 is the expected number of each of the blue cards per box. 

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