Bob Coyne wrote:Randy wrote:Originally posted by Bob Coyne: "The chance is 1/52 for a chosen card to be at a chosen number".
Correct me if I'm wrong but I believe that for a chosen card to be at a chosen number, the odds are MUCH higher than that. 52 cards to chose from located at 52 positions to chose from.......I'm not a statistical guy, but it's much more that a 1 in 52 shot. Right???
If the magician were to *predict* the card and position, then the probability of the spectator choosing those same values would be 1/2704 (1/52 times 1/52). So maybe that's what's confusing you.
In this case, however, the magician isn't predicting either the card or position, so all that matters is that the chosen card be at the chosen position. Since there are 52 positions, the chance that the chosen card is at any given position is 1/52. For example, let's say the spectator chooses AS and then randomly picks a position. One out of those 52 positions will give a match, so the chances of the AS of being at the chosen position is 1/52. The same is true for any chosen card. So no matter what card they choose, the probability is 1/52.
In this example, you are singling out the AS. I agree that the odds of the AS being at the chosen position are 1/52. The problem is, you don't know that the AS is going to be chosen. Once a card is chosen, you have 1/52 odds. Until that point, there are still 2704 possible combinations. The magician "predicting" is the same as the spectator randomly calling out a card and number.