A pack of cards consists of 52 different cards. A malicious dealer changes one of the cards for a second copy of another card in the pack and he then deals the cards to four players, giving therteen to each. The probability that one player has two identical cards is ?
2006-11-19 00:49:56 · 3 answers · asked by mongrel73 1 in Science & Mathematics ➔ Mathematics
I think this is only hard if you make it hard, but it's quite easy if you look at it in the right way. Since the order the cards are dealt in is arbitrary, you can assume that that the first card that was dealt was one of the two identical ones, and we can call the person who received it 'Alan' (note we are naming him AFTER he got the card, so we're not finding the probability of it going to a particular player). There are now 51 equally likely 'slots' that the other identical card can go in, and 12 of them are 'slots' that would give Alan the other identical card. So the probability is 12/51 .
2006-11-19 00:54:28 · answer #1 · answered by THJE 3 · 0⤊ 0⤋
NWordJim places unneeded restrictions on his solution. We can just say that SOME player will get one of the duplicate cards, without it having to be the first card in the deck. Then, the probability that the same player will get the other duplicate is 12/51. Also, there is no need to give the player a name, as you can see.
2006-11-19 01:05:38 · answer #2 · answered by ? 6 · 0⤊ 0⤋
hope I'm lucky ill wager 40%
2006-11-19 01:24:42 · answer #3 · answered by bigfat40 2 · 0⤊ 0⤋