# Math Help - Card game probability question

1. ## Card game probability question

I've not done probability in a while and looking at online examples I don't know if I'm doing everything right so maybe you can can help me out with the formula and explanation.

I'm a big fan of the game Magic the Gathering and when playing the game I like a healthy number of "land" cards in my opening hand. There are 60 cards in my deck and 26 land cards I've put in. What is the probability I will have 3 land cards in my opening hand (7 cards)? What about 2 land cards? What about atleast 2 land cards? Thanks in advance.

2. Originally Posted by XIII13Thirteen
I've not done probability in a while and looking at online examples I don't know if I'm doing everything right so maybe you can can help me out with the formula and explanation.

I'm a big fan of the game Magic the Gathering and when playing the game I like a healthy number of "land" cards in my opening hand. There are 60 cards in my deck and 26 land cards I've put in. What is the probability I will have 3 land cards in my opening hand (7 cards)? What about 2 land cards? What about atleast 2 land cards? Thanks in advance.
Since I don't know anything about the game, would you clarify the problem statement, please?

Is the total number of card in the deck 60 (26 land plus 34 non-land), or 86 (60 non-land plus 26 land)?

3. Originally Posted by awkward
Since I don't know anything about the game, would you clarify the problem statement, please?

Is the total number of card in the deck 60 (26 land plus 34 non-land), or 86 (60 non-land plus 26 land)?
Sorry, I'll clarify. Also I apologize if I placed this in the wrong forum. I saw the basic probability forum questions above just today. Anyway, onto the clarification.

Total cards in the deck: 60 (26 land and 34 non-land)
Opening hand: 7 cards

4. Originally Posted by XIII13Thirteen
Sorry, I'll clarify. Also I apologize if I placed this in the wrong forum. I saw the basic probability forum questions above just today. Anyway, onto the clarification.

Total cards in the deck: 60 (26 land and 34 non-land)
Opening hand: 7 cards
Let's say the number of land cards in your hand is x. Then we are dealing with a hypergeometric distribution, and

$p(x) = \frac{\binom{26}{x} \binom{34}{7-x}} { \binom{60}{7}}$

For x = 0 to 7, this yields p(x) =
0.0139, 0.0905, 0.2342, 0.3122, 0.2316, 0.0956, 0.0203, 0.0017.

To find the probability that you have at least 2 land cards, you could either add up p(x) for x = 2 to 7, or you could save computation by using

$P(X \ge 2) = 1 - P(X = 0) - P(X = 1)$.