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Claudio Inner circle Europe 1927 Posts |
I read about Terry LaGerould’s effect Please Don't Match, and I need some help about its probabilities.
In a nutshell, 14 cards are torn in half and the halves are mixed together. The halves are then placed in the performer’s pocket who bets that he’ll be able to pull out of his pocket, one at a time, 7 halves and that none will match, i.e no two halves will come from the same card. The performer wins his wager. I was trying to work out the probabilities, not only for each draw: 1, 2, … 7, but as well for the whole series. What’s the probability that there will be at least a match? Thank you. |
Claudio Inner circle Europe 1927 Posts |
Sorry, I meant, 7 cards are torn in two, therefore there are 14 halves.
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Claudio Inner circle Europe 1927 Posts |
Ok, here's what I've worked out:
1-((14*12*10*8*6*4*2)/(14*13*12*11*10*9*8)) = 413/429 = 0.96. So, if I'm right, over 7 draws, the probability of drawing at least one pair of matching halves, to form a card, is 96%. The odds are massively stacked in favour of the spectator, as 96 times out of 100 bets, the performer "should" lose. |
Jimso New user 75 Posts |
Your logic is correct, provided that each card is drawn independently and the probability of drawing any card from those remaining is equal. Those are typical assumptions for combinatorial probabilities, but would be wrong if, for example, you could gain information from any of the drawn cards.
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WayneBurrows New user Palmerston North, New Zealand 72 Posts |
An alternative calculation (or rather explanation) is:
first card can be anything probability 1 second card can be 12/13 remaining third card 10/12 remaining etc 1 * 12/13 * 10/12 * 8/11 * 6/10 * 4/9 * 2/8 = 16/429 (as above). This is the probability of getting pieces from seven different cards. |
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