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Interesting Probability

52 cards in a deck. Dealer switches one card for a copy of another card in the deck (so there are 2 identical cards in the deck). He deals 13 cards to 4 players. What is the probability that a player gets two identical cards.

a- 3/13
b- 12/51
c-1/4
d-13/51

I am getting 2/13 which is none of the options. Please help
Reply 1
Original post by dennisgwa32
52 cards in a deck. Dealer switches one card for a copy of another card in the deck (so there are 2 identical cards in the deck). He deals 13 cards to 4 players. What is the probability that a player gets two identical cards.

a- 3/13
b- 12/51
c-1/4
d-13/51

I am getting 2/13 which is none of the options. Please help


Is that the whole question? Can you type out the whole question in full, because none of the options seem right for the type of question. They're all far too large. The probabilty of drawing two identical cards is quite small unless it's two identical cards in terms of number, colour or suit .
Reply 2
Original post by Shiv7
Is that the whole question? Can you type out the whole question in full, because none of the options seem right for the type of question. They're all far too large. The probabilty of drawing two identical cards is quite small unless it's two identical cards in terms of number, colour or suit .

The full question is attached. But I wrote it out pretty much in full.
Reply 3
Original post by dennisgwa32
The full question is attached. But I wrote it out pretty much in full.


Oh sorry. Is the answer (c) by any chance?
Reply 4
Original post by Shiv7
Oh sorry. Is the answer (c) by any chance?

I’m not asking for an answer. I don’t know the answer - there is no mark scheme. I’m asking for an explanations
Original post by dennisgwa32
I’m not asking for an answer. I don’t know the answer - there is no mark scheme. I’m asking for an explanations


What was your method and thinking for getting 2/13?
Reply 6
Original post by dennisgwa32
I’m not asking for an answer. I don’t know the answer - there is no mark scheme. I’m asking for an explanations


Right okay, my answer would be 1/4. Explanation is as follows.
There are 4 people in the game and there are 2 identical cards. Hence the probabilty of any one individual to have two of these cards must be 1/4?
Original post by Shiv7
Right okay, my answer would be 1/4. Explanation is as follows.
There are 4 people in the game and there are 2 identical cards. Hence the probabilty of any one individual to have two of these cards must be 1/4?


Imagine a scenario where the two identical cards are at the top of the pack, ready to be dealt. The dealer starts dealing... Player one gets the first identical card, player two the second, and all the rest are dealt accordingly. In this case no player gets both identical cards. So I don't think it's as simple as that :beard:
Original post by Shiv7
Right okay, my answer would be 1/4. Explanation is as follows.
There are 4 people in the game and there are 2 identical cards. Hence the probabilty of any one individual to have two of these cards must be 1/4?


lol

that's not how probability works.

At the OP: you need to figure out the chances card by card. I would start by assuming without loss of generality that the very first card dealt to player 1 is one of the two identical cards.

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