# What is the probability that a bridge hand contains no Aces, Kings, Queens, Jacks, or Tens .?

This is how I calculated it.

There are 5 card values we don't want (Aces, Kings, Queens, Jacks, or Tens).

There are four suits (Hearts, Queen, King, Spades).

Therefore there are 20 cards we don't want.

So the number of bridge hands that don't contain Aces, Kings, Queens, Jacks or Tens

is {32 choose 13} .

So Probability (bridge hand with no Aces,Kings,Queens,Jacks, or Tens) = {32 Choose 13} / {52 Choose 13}

If anyone got something else please tell me.

### 2 Answers

- joshLv 510 years agoBest Answer
I'm not statistics expert, but I would be inclined to think of it like this:

There are 20 cards you don't want, so 32 you do. Your odds of the first card in your hand being one that you want is:

32/52, the odds of the second being one that you want is then:

31/51, and so on, each time both the numerator and denominator decrease by one because there would be one less of the "good" cards, and one less card overall.

If you continue to do that for 13 cards, you arrive at the same answer you did.

I guess you're right. As I said, I'm no statistics expert!

- AngelaLv 44 years ago
That's when you need a poker face. Make them think you have nothing, and raise the pot, higher and higher, till they're all in.