Trading Card Game: Probability of Rares!

[RayZorback]

Hey everyone. I've never been great at Math & I need some Help. This is NOT a homework question. I'm actually out of college - you'd be surprised at what you forget!

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??

THANK YOU FOR YOUR HELP! (I wish I had paid more attention in school!!)

Bye for now,
Ray

 

[Denis]

Well, the way I see it, your problem can be simplified to:
- 8 boxes (all look the same)
- 1 contains 15 red cards labelled 1 to 15
- 7 contain 53 blue cards labelled 1 to 53

If 1 box 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

However, I'm no expert in probabilities, and if that's wrong, I'm sure an expert (such as Sir Skeeter)
will jump in, bring it to our attention, and supply you with a probability gem!

 

[RayZorback]

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? If I don't think my calculator will do that 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.

Thanks!!!