I'm posting one puzzle, riddle, math, or statistical problem a day. Try to answer each one and post your answers in the comments section. I'll post the answer the next day. Even if you have the same answer as someone else, feel free to put up your answer, too!
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Here's an attempt...
ReplyDeleteYour chances are 1/53 if the King of Hearts was not the card you moved from pack A to pack B, and 2/53 if it is the card you moved. The odds of the King of Hearts being the card you moved over are 1/51 (since you eliminated the Queen of Hearts). So I'd say the chances are:
(1/53 * 50/51) + (2/53 * 1/51) = .01924ish
Andy has explained with very well, and I reached the same equation.
ReplyDeleteSO I guess that is the answer.
.01924....
www.guessthelogo.blogspot.com
is it.. 52 / (51 * 53)
ReplyDeleteThis is a little tricky. The answer is 1/53 + (1/53 * (1/51)) which reduces to 52/2703 or approximately 1.92378838%.
ReplyDeleteThe trick is this. If the top card of A is the Queen of Hearts then the chances that we picked the King of Hearts out of A and put it into B is 1/51. The chances of picking the King of Hearts from the original B deck are 1/53 (53 because we added the card from A) and the chances that we pick the a King of Hearts from A shuffled into B is 1/51 * 1/53. So the total chances are 1/53 + 1/53 * 1/51.
The big trick is the Queen of Hearts. If the question said that you turned up some random card from A then the answer would be 1/53 + 1/53 * 1/52. But since we know it is the Queen then we know that the card we took from A is not the Queen so it is one of the 51 other cards in the deck.