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Turk Inner circle Portland, OR 3546 Posts |
There is an effect where you, the magician has 5 different cards (A, 2, 3, 4 and 5) and the spectator has the same 5 cards. If the magician lays down all five of his cards face down in a row and the spectator then place one of his cards on each of the magician's 5 cards (so you end up with 5 piles of two cards each), what is one the probability that all five piles will contain a match? In other words, if the magcian laid his cards face down in a row and the cards were laid out as 3, Ace, 2, 4 and 5, what is the probability that the spectator would also lay the matching card down on top of each of the 5 cards so that you'd end up with 5 matched piles of 3, Ace, 2, 4 and 5?
A friend of mine says the odds are 5 X 4 X 3 X 2 X 1 = 120 to 1. Although I can't fault the logic or the math, this seems a lot lower than I'd have expected. Is 120 to 1 the correct probability? Thanks for the info. Mike
Magic is a vanishing Art.
This must not be Kansas anymore, Toto. Eschew obfuscation. |
rgranville Elite user Boston area 463 Posts |
There are indeed 120 different ways to arrange five cards, and the probability of a random arrangement matching another is 1/120, or 0.00833333333333333. The odds are 119 to 1. That is, in a fair game, if you bet $1 that the two arrangements match, I should pay you $119 (plus the dollar you bet) whenever you're right, and keep your dollar when you're wrong. Over the long haul, we should break even.
:banana: |
Heinz Weber New user Austria 83 Posts |
There are 120 different permutations for 5 cards, that's correct. So in 1 out of 120 tries you get the 'perfect match'. But there's a better way for betting on matches like this: the probability for 1 pair out of these 5 is approx. 63%!
Heinz |
stanalger Special user St. Louis, MO 998 Posts |
To clarify Heinz Weber's previous post:
The probability of AT LEAST ONE match (out of 5) is approx. 63% The probability of EXACTLY ONE match is 45/120 (37.5%) The probability of EXACTLY TWO matches is 20/120 (approx. 16.7%) The probability of EXACTLY THREE matches is 10/120 (approx. 8.3%) The probability of EXACTLY FOUR matches is 0 The probability of EXACTLY FIVE matches is 1/120 (approx. 0.8%) Stan Alger |
Heinz Weber New user Austria 83 Posts |
Thank you Stan, that's what I tried to say!
Heinz |
Turk Inner circle Portland, OR 3546 Posts |
Thanks, Guys. I appreciate the info.
Mike
Magic is a vanishing Art.
This must not be Kansas anymore, Toto. Eschew obfuscation. |
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