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# Harry has 6 different pairs of shoes, 2 pairs are pink. If he selects

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Re: Harry has 6 different pairs of shoes, 2 pairs are pink. If he selects [#permalink]
Bunuel wrote:
Harry has 6 different pairs of shoes, 2 pairs are pink. If he selects 2 individual shoes at random and without replacement, what is the probability that he selects a matching pink pair ?

A. 1/6
B. 1/9
C. 1/11
D. 1/33
E. 1/36

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Anyone else want to try?
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Re: Harry has 6 different pairs of shoes, 2 pairs are pink. If he selects [#permalink]
Why D?
6 pairs = 12 shoes
C(4,2) / C (12 / 2) = 1 / 11
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Harry has 6 different pairs of shoes, 2 pairs are pink. If he selects [#permalink]
Sigh like with all the Probability and combination questions the answer seems so obvious after youve got it wrong once .

Got it wrong on the first try picked C

2nd try -

Total no of shoes = 6* 2 = 12
No of pink shoes = 2*2 = 4

Probability of picking a matching pair = prob of picking a pink shoe * Prob of picking the shoe that forms the pair for picked shoe
= 4/12 * 1/11 (as only one of the remaing 11 will form a pair with the first shoe)
= 1/33
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Re: Harry has 6 different pairs of shoes, 2 pairs are pink. If he selects [#permalink]
6 pairs = 12 shoes
select one pink shoe = 4/12 = 1/3
selecting its matching pink shoe = 1/11 (since we need to make matching pair)

probability of selecting this pair = 1/3*1/11 = 1/33
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Harry has 6 different pairs of shoes, 2 pairs are pink. If he selects [#permalink]
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Given: Harry has 6 different pairs of shoes, 2 pairs are pink.
Asked: If he selects 2 individual shoes at random and without replacement, what is the probability that he selects a matching pink pair ?

Total shoes = 6*2 = 12
Pink shoes pairs = 2

The probability that he selects a matching pink pair = 2C1/12C2 = 2/66 = 1/33

IMO D
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Re: Harry has 6 different pairs of shoes, 2 pairs are pink. If he selects [#permalink]
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Bunuel wrote:
Harry has 6 different pairs of shoes, 2 pairs are pink. If he selects 2 individual shoes at random and without replacement, what is the probability that he selects a matching pink pair ?

A. 1/6
B. 1/9
C. 1/11
D. 1/33
E. 1/36

There are 6 pairs, two are pink but each pair is distinct.
This means that we have 12 shoes out of which 4 are pink - Pink1Left, Pink1Right, Pink2Left, Pink2Right

We need to select a matching pink pair which means we need to select either {Pink1Left, Pink1Right} or {Pink2Left, Pink2Right}.

For our first pick, we can pick any one of the 4 pink shoes with the probability 4/12 = 1/3 (say we picked up Pink1Right)

For our second pick, we must now pick only Pink1Left. There is only 1 way to correctly make a matching pink pair out of the leftover 11 shoes now. So probability = 1/11

Total Probability of picking a matching pink pair = (1/3) * (1/11) = 1/33

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Harry has 6 different pairs of shoes, 2 pairs are pink. If he selects [#permalink]
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Bunuel wrote:
Harry has 6 different pairs of shoes, 2 pairs are pink. If he selects 2 individual shoes at random and without replacement, what is the probability that he selects a matching pink pair ?

A. 1/6
B. 1/9
C. 1/11
D. 1/33
E. 1/36

Total possible selections = $$^{12}C_2$$ = 66

Number of favorable outcomes = 2 (i.e. one for each pair)

Required Probability = $$\frac{2}{66}$$ = $$\frac{1}{33}$$

Option D
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Re: Harry has 6 different pairs of shoes, 2 pairs are pink. If he selects [#permalink]
It could also be

-> 2/12X1/11 FOR ONE PAIR, then for the second pair there will be another similar outcome

so 1/66X2 = 1/33.

Is this approach right?
I am assuming two outcomes

Leftpink, rightpink

and

RightPink, Leftpink
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Re: Harry has 6 different pairs of shoes, 2 pairs are pink. If he selects [#permalink]
Posted from my mobile device
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17093915468942667513882609869633.jpg [ 2.79 MiB | Viewed 1396 times ]

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Re: Harry has 6 different pairs of shoes, 2 pairs are pink. If he selects [#permalink]
PS31 wrote:
Posted from my mobile device

If anyone wants an explanation, happy to do it.
Re: Harry has 6 different pairs of shoes, 2 pairs are pink. If he selects [#permalink]
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