Bridge Hand

• Feb 7th 2011, 08:27 PM
divinelogos
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?
• Feb 8th 2011, 08:17 AM
theodds
Quote:

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.
• Feb 8th 2011, 08:47 AM
Unknown008
Yep, otherwise, you'll end up with a probability greater than 1!
• Feb 8th 2011, 05:46 PM
divinelogos
hmm i think i have it right. it just means it's REALLY going to happen ;)

all kidding aside, thank you for the confirmation!