# Math Help - Bridge Hand

1. ## 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?

2. 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.

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

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

all kidding aside, thank you for the confirmation!