Can anyone help me with one Probability question please?

The questions is as follows: 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 thirteen to each. the probability that one player has two identical cards is?

Can anyone think of an answer to solve this problem? Any help would be really appreaciated!! :smile:

Reply 1

Anarchy Everywhere

Hmmm, Binomial Distribution is out of the question so I'm not sure, it's an odd question too as the way the cards are dealt will have an effect on the probability too I think.

Reply 2

cnoliverlee

I got really confused on probability questions. don't like them at all

Reply 3

James

This is the same question as:

There are 52 marbles in a bag. Fifty are red, and two are blue. If I take thirteen marbles at random, what is the probability that the selection includes both blue marbles?

Reply 4

Fertil3

There are 52 cards in a pack. The probability of getting a card of a certain number and certain suit is going to be 1/52 yes? The probability of getting a certain number but not a certain suit will be 4/52.

Now... the probability of getting two of the same number (specific) is the same as 4/52 x 4/52 (=16/2704). There are 13 different cards in the pack so multiply the numerator by 13 (=208/2704 OR 1/13). Notice anything?

Anyway... that was the basic stuff behind the probability of the cards before the dealer changed anything. Bear in mind, he changes only 2 NUMBERS. He removes 1 NUMBER and replaces it with ANOTHER. So he changes the one he takes away and changes the one he adds a copy of.

So we'll do the same as above. 13-2=11. 11 numbers are still exactly the same as before. So

11 x 16/2704 = 176/2704

Keep that fraction (or probability) in mind.

Now, the probability of getting two of the card he removes is 3/52 x 3/52 = 9/2704.
Likewise the probability of getting two of the card he adds a copy of is 5/52 x 5/52 = 25/2704.

Kk, now before looking at the spoiler I want you to make sure you understand everything lol.

Spoiler