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# What is the probability of getting two cards that belong to the same

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What is the probability of getting two cards that belong to the same  [#permalink]

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15 Jun 2011, 21:48
7
00:00

Difficulty:

75% (hard)

Question Stats:

46% (01:25) correct 54% (01:34) wrong based on 121 sessions

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What is the probability of getting two cards that belong to the same color when two cards are drawn at random from a pack of 52 cards?

A. 1/2

B. 25/51

C. 26 C 2 / 52 C 2

D. 1/26

E. 25/52

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Re: What is the probability of getting two cards that belong to the same  [#permalink]

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15 Jun 2011, 22:42
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soaringAlone wrote:
What is the probability of getting two cards that belong to the same color when two cards are drawn at random from a pack of 52 cards?

A. 1/2

B. 25/51

C. 26 C 2 / 52 C 2

D. 1/26

E. 25/52

The wording of the question is strange. I guess by 'belong to the same color', they mean that you either pick two red cards, or two black cards. In a standard deck of cards there are 26 red cards and 26 black cards -- note that you do *not* need to know anything at all about standard decks of cards on the GMAT.

Now the first card we pick doesn't matter. We only want to make sure our second card is the same colour as whatever we picked first. When we pick our second card we are selecting from the 51 remaining cards, and there are 25 cards left which are the same colour as the first card we picked, so the answer must be 25/51.

You've cited the OA as 'C', which is not correct. Answer choice C is the probability of picking, specifically, two red cards (or equivalently, it's the probability of picking two black cards). The correct answer is exactly twice as large as answer choice C.
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Re: What is the probability of getting two cards that belong to the same  [#permalink]

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06 Oct 2017, 07:52
In a pack of 52 cards, there are 26 black cards (13 spade and 13 club), and 26 red cards (13 heart and 13 diamond).

Now, the probability of selecting 1st card from 52 cards: 1;

Remaining cards of same colors = 25; Total remaining cards = 51;
So, the probability of selecting 2nd card of same color = 1*25/51 = 25/51

Ans: B.
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Re: What is the probability of getting two cards that belong to the same  [#permalink]

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01 Feb 2018, 02:29
Total ways = 52C2
Selecting both Red cards = 26C2
Selecting both Black cards = 26C2
Probability = (2 x 26C2)/52C2 = 25/51
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Re: What is the probability of getting two cards that belong to the same  [#permalink]

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02 Feb 2018, 12:18
2
soaringAlone wrote:
What is the probability of getting two cards that belong to the same color when two cards are drawn at random from a pack of 52 cards?

A. 1/2

B. 25/51

C. 26 C 2 / 52 C 2

D. 1/26

E. 25/52

We must assume that half of the cards are red and half are black.

The probability of getting two red cards is 26/52 x 25/51 = 1/2 x 25/51 = 25/102.

Since the number of black cards is the same as the number of reds, the probability of selecting two black cards is also 25/102.

So the probability of selecting two cards of the same color (either both red or both black) is 25/102 + 25/102 = 25/51.

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Re: What is the probability of getting two cards that belong to the same  [#permalink]

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10 Mar 2019, 10:45
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Re: What is the probability of getting two cards that belong to the same   [#permalink] 10 Mar 2019, 10:45
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