Thread: Bridge Hand

What is the probability that a dealt bridge hand of 13 cards will contain no diamonds or hearts?


Attempt 1: Divide possible outcomes by favorable outcome:

I reasoned as follows. There are 52 choose 13 number of hands so this is the number of possible outcomes. I want to divide this by the number of hands containing only spades and clubs (in other words no diamonds or hearts). Thus, there are only 26 cards I can choose from to get these hands. So the favorable outcomes are 26 choose thirteen. The answer being (52 choose 13)/(26 choose 13).


Do I have the right idea?

Originally Posted by divinelogos

What is the probability that a dealt bridge hand of 13 cards will contain no diamonds or hearts?


Attempt 1: Divide possible outcomes by favorable outcome:

I reasoned as follows. There are 52 choose 13 number of hands so this is the number of possible outcomes. I want to divide this by the number of hands containing only spades and clubs (in other words no diamonds or hearts). Thus, there are only 26 cards I can choose from to get these hands. So the favorable outcomes are 26 choose thirteen. The answer being (52 choose 13)/(26 choose 13).


Do I have the right idea?

That is the right idea, but you need to flip the fraction. The answer you gave is greater than 1.

Yep, otherwise, you'll end up with a probability greater than 1!

hmm i think i have it right. it just means it's REALLY going to happen


all kidding aside, thank you for the confirmation!