You're playing bridge - four players, 52 cards, each player is dealt 13 cards.

You deal the cards and your right-hand opponent picks up his hand. For reasons known only to him he announces, truthfully, "I have an ace." Given only that information (nobody else has looked at their cards), sufficient skill, and appropriate motivation, you could calculate the probability that he has a second ace.

Call that probability A.

Later, it's your deal again. You deal the cards and your right-hand opponent picks up his hand. For reasons known only to him he announces, truthfully, "I have the ace of clubs." Given only that information (nobody else has looked at their cards), sufficient skill, and appropriate motivation, you could calculate the probability that he has a second ace.

Call that probability B.

The question before you is this: How do these two probabilities compare? Is A greater than B? Is B greater than A? Or are they equal?

Whaddaya think?

FAQs

Is there something special about the ace of clubs?

No. The only important point is that on the second deal he mentioned the suit of the ace. He could have said diamonds, hearts, or spades without affecting the value of B.

Is there something special about the aces?

Apart from the fact that in bridge the ace is the highest-ranking card in its suit, no. The question (about the probabilities) would be the same if he'd mentioned deuces, eights, or any other rank. That aces are valuable both makes the question more interesting and your opponent's declarations more bizarre.

 

i say they're equal.

 

The probability of me reading past the first paragraph...ZERO!



Warren

 

All of the above.

 

I lack the appropriate motivation.

 

definitely equal

 

Definitely not equal, in point of fact.

 

i've never taken probability but i'd have to guess not equal..since you didnt say it was shuffled you'll have to asume they are all in order so someone and only someone has 4 aces

 

One always shuffles before dealing in bridge. And one's right-hand opponent cuts the cards before the deal.

 

There are 6 combinations of 2 aces. The first case, the stater has all 6 available to him. The second case, the stater has only 3 combinations available to him. First probability is double the second.