- 225

- 0

You have a 52 cards deck and you draw 3 random cards from it. What are the probabilities of the following (order doesn't matter in all of them):

1. Drawing two specific cards (suit doesn't matter) with the third one being any other card. For example 6 9 x or 9 6 x or x 6 9, etc..

2. Drawing two specific cards (ie. 4&5, 8&3, etc..) with the third one being any other card and having all three cards be of different suits.

2. Drawing two specific cards of the same suit (ie. 6 of spades and 9 of spades, 4 of hearts and 7 of hearts, etc..) with the third one being any other card with a different suit.

I'm more interested in knowing how to calculate those probabilities than in just knowing the probabilities, so if you can show me how to calculate all 3 of them that would be great!

Edit: for the first condition, the third card (x) can be one of the two cards selected (ie. 6 9 9 is valid).

1. Drawing two specific cards (suit doesn't matter) with the third one being any other card. For example 6 9 x or 9 6 x or x 6 9, etc..

2. Drawing two specific cards (ie. 4&5, 8&3, etc..) with the third one being any other card and having all three cards be of different suits.

2. Drawing two specific cards of the same suit (ie. 6 of spades and 9 of spades, 4 of hearts and 7 of hearts, etc..) with the third one being any other card with a different suit.

I'm more interested in knowing how to calculate those probabilities than in just knowing the probabilities, so if you can show me how to calculate all 3 of them that would be great!

Edit: for the first condition, the third card (x) can be one of the two cards selected (ie. 6 9 9 is valid).

Last edited: