Probability of Drawing X cards in a deck...

Quick intro to the question. I play a card game called Magic the gathering, and I am hoping to find a mathematical solution to an issue I am having. So a player has a deck of 60 cards and you start the game by drawing 7 of these to be your hand, so now the new total of the cards in the deck are 57. Here is where we will start the question.

Q: I play a card "Oath of Nissa" that lets me look at the top 3 cards of a deck of 57. I can grab one type(x) of card from this three and add it to my hand. If I have 48 of this type(x) of card what is the probability I will hit one of these types every time I play the "Oath of Nissa"?

Reason for question expanded. I am trying to improve my deck for upcoming tournament and I am wondering how many type(x) I should in my deck to utilize Oath of Nissa effectively to where I am almost never unable to find a type(x) in the three I get to look at. My apologies if I worded this question incorrectly.

Jonathandj20 said:

Quick intro to the question. I play a card game called Magic the gathering, and I am hoping to find a mathematical solution to an issue I am having. So a player has a deck of 60 cards and you start the game by drawing 7 of these to be your hand, so now the new total of the cards in the deck are 57. Here is where we will start the question.

Q: I play a card "Oath of Nissa" that lets me look at the top 3 cards of a deck of 57. I can grab one type(x) of card from this three and add it to my hand. If I have 48 of this type(x) of card what is the probability I will hit one of these types every time I play the "Oath of Nissa"?

Click to expand...

What is a "type(x) of card"? How many types are there? How many of each type? How do you "have 48 of this type(x) of card" when your hand contains only seven cards? If you've drawn seven from a stack of sixty, how are there still fifty-seven left in the stack?

When you reply, please include a clear listing of your thoughts and efforts so far. Thank you!