My Math Forum  

Go Back   My Math Forum > College Math Forum > Advanced Statistics

Advanced Statistics Advanced Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
June 18th, 2008, 08:43 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
RayZorback is offline  
 
June 18th, 2008, 05:59 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.
cknapp is offline  
June 18th, 2008, 06:18 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!
RayZorback is offline  
June 30th, 2008, 01:49 PM   #4
Global Moderator
 
CRGreathouse's Avatar
 
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.
CRGreathouse is offline  
Reply

  My Math Forum > College Math Forum > Advanced Statistics

Tags
card, game, probability, trading



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
how to solve this card game probability problem davedave Probability and Statistics 7 March 14th, 2012 09:36 AM
Winning Strategy of A Card Game tagitables Advanced Statistics 1 February 22nd, 2012 02:23 PM
Card Game - settle an argument gmpco Advanced Statistics 4 February 13th, 2012 08:04 PM
Card game Combinatorics eternity Algebra 1 August 6th, 2010 01:46 PM
Probability in a Trading Card Game?? RayZorback Algebra 1 June 18th, 2008 08:48 AM





Copyright © 2019 My Math Forum. All rights reserved.