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total shoes 12
ways to select 2 pink: 4*3=12
total possibilities: 12*11
So final solution: 12/(12*11) = 1/11
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Bunuel
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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Why D?
6 pairs = 12 shoes
C(4,2) / C (12 / 2) = 1 / 11
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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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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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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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Bunuel
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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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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why can't we do (4C1 * 1)/12C2 which gives 2/33 ?
where am i going wrong? kindly help.
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abcd1234!!
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

why can't we do (4C1 * 1)/12C2 which gives 2/33 ?
where am i going wrong? kindly help.


In the denominator, you have the number of different pairs possible from 12 shoes. However, in the numerator, it should be 2C1, representing the number of ways to select 1 matching pink pair from the 2 available pairs (either P1_Left and P1_Right OR P2_Left and P2_Right).
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Bunuel KarishmaB what is question told that 2 pair pink color shoes is identical to each other expect the left and right shoes!! what will be the probability of selecting a perfect pink color shoe pair?
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Vibhatu
Bunuel KarishmaB what is question told that 2 pair pink color shoes is identical to each other expect the left and right shoes!! what will be the probability of selecting a perfect pink color shoe pair?
Then the probability of the second shoe will simply become 2/11 both either of the two pinks of the other foot will work since both pairs are identical.
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Ans will be 2C1/12C2
this 2C1 will be any of the pink pair
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Amazing explanation! Thank you
KarishmaB
Bunuel
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

Answer (D)
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