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03 Feb 2023, 13:20
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
58% (01:42) correct
42%
(01:37)
wrong
based on 555
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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
A. 1/6
B. 1/9
C. 1/11
D. 1/33
E. 1/36
06 Feb 2023, 09:31
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Bunuel Although I solved the problem as others have done it, upon carefully reading the problem statement I observed that the question mentions different pairs and matching pair.
So I tried to break the problem as below:
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.
Posted from my mobile device
So I tried to break the problem as below:
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.
Posted from my mobile device
07 Feb 2023, 23:35
Kudos
Bookmarks
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
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)
