My Math Forum Probability in a Trading Card Game??

 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:- 1 box of 36 packs of 15 cards (all packs look the same) - 1 in 8 packs of cards contain 1 of 15 red cards labelled 1 to 15 - 7 in 8 packs of cards contain 1 of 53 blue cards labelled 1 to 53 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 (1.41083E-75 ??). Or, do I say (1/120)*36 = 0.3? For the blue cards: (7/424) * 36 = .59 & (7/424)^36= 6.89221E-65 ?? The number that spits out in the end, what unit is it? 0.3 of a what? or 1.41083E-75 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:
 Originally Posted by RayZorback I think I would use (1/120)^36? Which equals a number I don't under stand (1.41083E-75 ??). Or, do I say (1/120)*36 = 0.3?
Yes, add the probabilities. (1/120)^36 would be correct if you want all of the packs to have the "correct" type of card.
And by the way, 1.41... E-75 means 1.41...* 10^(-75)

Quote:
 For the blue cards: (7/424) * 36 = .59
That is correct

Quote:
 The number that spits out in the end, what unit is it? 0.3 of a what? or 1.41083E-75 whats?
There are no units. It's a probability of occurrence. So there is a .3 chance of selecting the card you want. Or, make it a percentage: there is a 30% chance.

Quote:
 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."
It doesn't always pan out to a 1 in ___ chance, although you could have something like "you have a __ in __ chance..." etc.

 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.

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post davedave Probability and Statistics 7 March 14th, 2012 08:36 AM tagitables Advanced Statistics 1 February 22nd, 2012 01:23 PM gmpco Advanced Statistics 4 February 13th, 2012 07:04 PM eternity Algebra 1 August 6th, 2010 12:46 PM RayZorback Algebra 1 June 18th, 2008 07:48 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top