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

Question

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

Ic0830de · Accepted Answer

Total shoes: 12(6 pairs)

Step 1: there are 4 possibilities to pick a pink shoe.
So 4/12

Step 2: now the probability that the second shoe picked is pink and a match to the first picked shoe is 1/11 ( without replacement we have 11 shoes remaining) but there is only 1 out of those which will be a match. 
So the answer is: 1/33

PS: had the question not mentioned different pairs and matching pair, 1/11 would have been correct.

Not sure if my analysis is correct. But I tried to reverse engineer from the answer to the steps.

KarishmaB · Answer

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)

SignUp · Answer

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

Kinshook · Answer

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

gmatophobia · Answer

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

abcd1234!! · Answer

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

Bunuel · Answer

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).

Vibhatu · Answer

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?

KarishmaB · Answer

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.

dec2023 · Answer

Hi gmatophobia, I used combination method as well but I got it wrong at this part:

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

In my understanding, number of favourable outcomes will be:
4C1 (choose 1 shoe out of 4 pink shoes) x 1 (only 1 option that will pair with the selected shoe)

Can you please help me to understand why did you use 2C1 when there are 4 available options to choose from?

Thank you in advance 🙏

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards