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John draws two cards at random from a pack of 52 cards. After returnin

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John draws two cards at random from a pack of 52 cards. After returnin  [#permalink]

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New post 26 May 2018, 11:01
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John draws two cards at random from a pack of 52 cards. After returning them to the pack and shuffling it, George draws two cards at random. The probability that they have exactly one common card is:-
A) \(\frac{25}{546}\)
B) \(\frac{25}{663}\)
C) \(\frac{48}{663}\)
D) \(\frac{50}{663}\)
D) None of these

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Re: John draws two cards at random from a pack of 52 cards. After returnin  [#permalink]

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New post 26 May 2018, 20:20
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gmatbusters wrote:
John draws two cards at random from a pack of 52 cards. After returning them to the pack and shuffling it, George draws two cards at random. The probability that they have exactly one common card is:-
A) \(\frac{25}{546}\)
B) \(\frac{25}{663}\)
C) \(\frac{48}{663}\)
D) \(\frac{50}{663}\)
D) None of these



ways to pick two cards = \(52C2=\frac{52*51}{2}=26*51\)
let one is common so 2 ways and the second one can be any of the remaining 50 so \(2*50\)

probability = \(\frac{2*50}{26*51}=\frac{50}{663}\)

D
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John draws two cards at random from a pack of 52 cards. After returnin  [#permalink]

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New post 22 Jun 2018, 15:02
chetan2u
Can you please check my answer:

We have 2 possibilities:
P of the first card is the common = (1/52)*(50/51)*2 ==> 2 for the sequence
P of the second card is the same.

Adding both: (1/52)*(50/51)*2*2 = 50/663
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Re: John draws two cards at random from a pack of 52 cards. After returnin  [#permalink]

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New post 22 Jun 2018, 18:53
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HisHo wrote:
chetan2u
Can you please check my answer:

We have 2 possibilities:
P of the first card is the common = (1/52)*(50/51)*2 ==> 2 for the sequence
P of the second card is the same.

Adding both: (1/52)*(50/51)*2*2 = 50/663



Yes HisHo you are correct...
p of first card as common = 2/52*50/51..
For second one = 50/52*1/51..
So total = 2*2/52*50/51=50/(51*13)
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Re: John draws two cards at random from a pack of 52 cards. After returnin  [#permalink]

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New post 22 Jun 2018, 23:41
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Basically, we can mark the cards mentally that were chosen in the first draw. Call them X and Y.

Now we need to choose exactly one out of these two: 2C1 ways
And choose another card from the remaining 50 cards: 50C1 ways
Total ways: 52C2

Prob = 2C1*50C1/52C2 = 50/663.

Answer = D
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Re: John draws two cards at random from a pack of 52 cards. After returnin  [#permalink]

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Re: John draws two cards at random from a pack of 52 cards. After returnin   [#permalink] 17 Jan 2020, 23:02
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