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July 17th, 2011, 01:02 PM   #11
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Re: Probability. A deck of card

Quote:
Originally Posted by greg1313
Quote:
Originally Posted by greg1313
P(j, q) = (1/52)*(1/52)
P(nj, q) = (51/52)*(1/52)
P(j, nq) = (1/52)*(51/52)
P(nj, nq) = (51/52)*(51/52)

P(j, q) + P(nj, q) + P(j, nq) + P(nj, nq) = 1.

P(j, q) + P(nj, q) + P(nj, nq) = 2653/2704.

I guess this is wrong, but can anyone tell me why?
Once a decision is made about one card, the second card has only 51 choices, not 52.
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July 17th, 2011, 01:10 PM   #12
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Re: Probability. A deck of card

I see, thanks. I was thinking that if you shuffle a deck of cards the odds of a queen of spades on the bottom would be 1/52 and 1/52 for a jack of clubs on top. It is interesting the sums of probabilities work out to 1 when added, using either interpretation. The results are close too.
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July 17th, 2011, 01:45 PM   #13
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Re: Probability. A deck of card

The probability for either is 1/52, but if we're creating a case where both happen then one unknown card has become known and there are only 51 possibilities for the second.

The probability of all possibilities in a situation sums to 1 (as it always should afaik), you are just describing a different situation. In yours a card is checked, then replaced and the deck is shuffled again before checking the second card. In the original a card is checked, but the deck is not shuffled before checking the other card. That means when we check the other side of the deck, we already know the card that occupied the top of the first side, so there's only 51 possible cards that could be the second card.
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July 17th, 2011, 01:53 PM   #14
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Re: Probability. A deck of card

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Originally Posted by hunnybee
A deck of card is shuffled. What is the chance that the top card is not the jack of clubs or the bottom card is the queen of spades?
So, after shuffling the deck, the probability of a queen of spades on the bottom is 1/52 and then 1/51 after you turn over the top card? That doesn't seem to account for the fact the top card might be the queen of spades.
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July 17th, 2011, 06:29 PM   #15
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If the top card is queen of spades, the chance that the bottom card is queen of spades is zero.
The chance that the top card is not queen of spades and the bottom card is queen of spades is (51/52)(1/51) = 1/52, as expected.
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