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June 18th, 2008, 06:09 AM   #1
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Probability in a Trading Card Game??

Hey everyone. I've never been great at Math & I need some Help. I'm in the process of writing an article and I need a little help finishing a math problem.

I play a trading card game with 4 "rarities": Mythic Rare, Rare, Uncommon, & Common.

I'm trying to calculate the probability of opening ONE PARTICULAR Mythic Rare in a Box of Booster Packs.
There are 36 Booster Packs in 1 Box.
Booster Packs contain
1 Rare/Mythic Rare (Supposedly 1 in 8 Booster Packs will contain a Mythic Rare.)
3 Uncommons
10 Commons
1 Mana
15 Cards total

There are 15 Possible Mythic Rares in the set of cards.
  • What is the probability of opening a particular Mythic Rare in the Booster Box?
    What is the probability of opening a particular "regular Rare?" (there are 53 possible Rares in a set of cards)

Here is what I have so far:
For the PARTICULAR Mythic Rare:
  • There is a 1:8 chance of getting a Mythic Rare in a booster pack: 12.5%
    So, in 36 Booster packs, I should open 4.5 (4 or 5 Mythic Rares)??
    There is a 1:15 chance of opening the PARTICULAR Mythic Rare I'm looking for: 6.67%
    12.5% * 6.67% = 0.83% (or 1/120) chance of opening a Particular Mythic Rare.
    But what about opening that Particular Mythic Rare in 36 booster packs?


For the PARTICULAR Regular Rare
  • There is a 7:8 chance of getting a Regular Rare in a booster pack: 87.5%
    So, in 36 Booster Packs, I should open 31.5 (31 or 32) regular rares??
    There is a 1:53 chance of opening the PARTICULAR Regular rare I'm looking for: 1.89%
    87.5% * 1.89% = 1.65% (or 7/424) chance of opening a Particular Regular Rare.
    But what about opening that Particular Regular Rare in 36 booster packs?


Is this math correct so far? Or am I totally confusing things??

What I'm not sure about is taking the next step to figure the packs in the box:
If my probability is 1:120 and I have 36 booster packs. Each with a 1:120 chance of getting the particular Mythic Rare (1/8 * 1/15). Wouldn't I multiply (1/120) * 36 = 0.3?
OR would I have (1/120)^36? I don't think my calculator will do the latter: 1.41083E-75 What??

If I use the (7/424) * 36 = .59
If I use (7/424)^36= 6.89221E-65 ??

What unit is it? What does it mean? 0.3 of a chance I get the particular Mythic Rare in 36 booster packs? 0.3% chance? I'm confused.

THANK YOU FOR YOUR HELP! (I wish I had paid more attention in school!!) Whoever answers the question right will get the credit in the article!!

Bye for now,
Ray
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June 18th, 2008, 08:48 AM   #2
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Re: Probability in a Trading Card Game??

I've simplified this question: http://www.mymathforum.com/viewtopic.php?f=24&t=3692
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