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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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26 May 2018, 11:01
1
4
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Difficulty:

95% (hard)

Question Stats:

38% (02:23) correct 62% (02:29) wrong based on 47 sessions

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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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26 May 2018, 20:20
1
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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22 Jun 2018, 15:02
chetan2u

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.

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

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22 Jun 2018, 18:53
1
HisHo wrote:
chetan2u

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.

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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22 Jun 2018, 23:41
2
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.

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

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17 Jan 2020, 23:02
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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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