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Tanya prepared 4 different letters to 4 different addresses. For each
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30 Aug 2013, 23:33
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48% (00:59) correct 52% (01:22) wrong based on 601 sessions
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Tanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address? A) 1/24 B) 1/8 C) 1/4 D) 1/3 E) 3/8 == Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
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Re: Tanya prepared 4 different letters to 4 different addresses. For each
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31 Aug 2013, 05:35



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Re: Tanya prepared 4 different letters to 4 different addresses. For each
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31 Aug 2013, 09:51



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Re: Tanya prepared 4 different letters to 4 different addresses. For each
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15 Sep 2013, 11:23
We are trying to find the probability of 1R3W.
Probability = number of ways to get 1R3W/number of ways total
number of ways total is 4! = 24. Imagine stuffing envelopes randomly. Stacy can put any of 4 letters into the first envelope, any of the remaining 3 into the next, either of the remaining 2 into the next, and has no choice to make on the last, or 4*3*2*1.
number of ways to get 1R3W : She could fill the first envelope with the right letter (1 way), then put either of the 2 wrong remaining letters in the next (2 ways), then put a wrong letter in the next (1 way). That's 1*2*1*1 = 2.
But since it doesn't have to be the first envelope that has the Right letter, it could be any of the 4 envelopes (i.e. we could have RWWW, WRWW, WWRW, WWWR), the total ways to get 1R3W is 4*2 = 8.
Probability is 8/24 = 1/3.



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Re: Tanya prepared 4 different letters to 4 different addresses. For each
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21 May 2014, 04:35
Aximili85 wrote: GODSPEED wrote: My 2 cents:
For 1 letter to go in right envelope  probability = 1/4 For 2nd letter to go in wrong envelope  probability = 2/3 For 3rd letter to go in wrong envelope  probability = 1/2 For 4th letter to go in wrong envelope  probability = 1
Now, in the order this arrangement can be done: C  Letter going into correct envelope W  Letter going into wrong envelope
No#1. C  W  W  W ............in correct envelope: 4* (1/4) * (2/3) * (1/2) * 1 = 1/3 Thats the only explanation i was able to understand =( I'm worried because if I don't learn the combinatrics formula way of doing it I might make a logical inconsistency while solving under a time limit. Just wondering, is the above method correct? What if the correct is not the first one? Does it change the procedure? Please advice Cheers! J



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Re: Tanya prepared 4 different letters to 4 different addresses. For each
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21 May 2014, 04:35
Aximili85 wrote: GODSPEED wrote: My 2 cents:
For 1 letter to go in right envelope  probability = 1/4 For 2nd letter to go in wrong envelope  probability = 2/3 For 3rd letter to go in wrong envelope  probability = 1/2 For 4th letter to go in wrong envelope  probability = 1
Now, in the order this arrangement can be done: C  Letter going into correct envelope W  Letter going into wrong envelope
No#1. C  W  W  W ............in correct envelope: 4* (1/4) * (2/3) * (1/2) * 1 = 1/3 Thats the only explanation i was able to understand =( I'm worried because if I don't learn the combinatrics formula way of doing it I might make a logical inconsistency while solving under a time limit. Just wondering, is the above method correct? What if the correct is not the first one? Does it change the procedure? Please advice Cheers! J



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Re: Tanya prepared 4 different letters to 4 different addresses. For each
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20 Sep 2014, 16:21
jlgdr wrote: Just wondering, is the above method correct? What if the correct is not the first one? Does it change the procedure? Please advice Cheers! J I actually had the same question and was about to post a reply on this thread seeking same but while typing it had the aha moment. Yes, even when one calculates the probability of each scenario separately, the total will be \(\frac{1}{3}\). #1  C W W W  \(\frac{1}{4}*\frac{2}{3}*\frac{1}{2}*1=\frac{1}{12}\) #2  W C W W  \(\frac{2}{4}*\frac{1}{3}*\frac{1}{2}*1=\frac{1}{12}\) (Note for the first W, desired outcomes are only two, the 3rd and 4th envelopes, and doesn't include its own envelope and the envelope for the second letter as that needs to have the correct one. Same explanation plays in scenarios #3 and #4) #3  W W C W  \(\frac{2}{4}*\frac{1}{3}*\frac{1}{2}*1=\frac{1}{12}\) #4  W W W C  \(\frac{2}{4}*\frac{1}{3}*\frac{1}{2}*1=\frac{1}{12}\)



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Re: Tanya prepared 4 different letters to 4 different addresses. For each
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01 Dec 2014, 02:09
Dienekes wrote: jlgdr wrote: Just wondering, is the above method correct? What if the correct is not the first one? Does it change the procedure? Please advice Cheers! J I actually had the same question and was about to post a reply on this thread seeking same but while typing it had the aha moment. Yes, even when one calculates the probability of each scenario separately, the total will be \(\frac{1}{3}\). #1  C W W W  \(\frac{1}{4}*\frac{2}{3}*\frac{1}{2}*1=\frac{1}{12}\) #2  W C W W  \(\frac{2}{4}*\frac{1}{3}*\frac{1}{2}*1=\frac{1}{12}\) (Note for the first W, desired outcomes are only two, the 3rd and 4th envelopes, and doesn't include its own envelope and the envelope for the second letter as that needs to have the correct one. Same explanation plays in scenarios #3 and #4) #3  W W C W  \(\frac{2}{4}*\frac{1}{3}*\frac{1}{2}*1=\frac{1}{12}\) #4  W W W C  \(\frac{2}{4}*\frac{1}{3}*\frac{1}{2}*1=\frac{1}{12}\) Bunuel, can you check this post, pls. I think there are mistakes in calculations of 2nd, 3rd, and 4th conditions. For the first W I think there must 3/4. Am I right?
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Re: Tanya prepared 4 different letters to 4 different addresses. For each
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14 Mar 2015, 09:53
Bunuel wrote: dk94588 wrote: Hello, this was on GMATprep, and I have had problems with this type of question before, but maybe you could help me solve it.
Tanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address?
A) 1/24 B) 1/8 C) 1/4 D) 1/3 E) 3/8 Total # of ways of assigning 4 letters to 4 envelopes is \(4!=24\). Only one letter in the right envelope: 4(# of envelopes)*2(# of ways possible to arrange 3 letters incorrectly in the envelopes, when one is correct). ABCD(envelopes)ACDB(letters) ADBC(letters) (When A is in the right envelope other three have only 2 possible incorrect arrangements) As we have 4 letters, total # of ways 4*2=8 \(P(C=1)=\frac{8}{24}=\frac{1}{3}\) Answer: D. All other possible scenarios: letterarrangementsunderstandingprobabilityandcombinats84912.htmlHope it's clear. Hi Bunuel, what if there were 5 letters and we were asked to find the same probability as in the original question , how would we calculate these possible wrong arrangements using combitronics ? (When A is in the right envelope other three have only 2 possible incorrect arrangements) ABCDE Total arrangements for BCDE=4! case 1: only 2 wrong : 4 case 2: three wrong : X so all wrong will be 4!4 X ? could you please help . thanks lucky



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Re: Tanya prepared 4 different letters to 4 different addresses. For each
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07 Jun 2015, 01:15
hard question, but if you do this two time, second time one month after first time, you can remember
I try to do this one for 3 times. now I master this problem



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Re: Tanya prepared 4 different letters to 4 different addresses. For each
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21 Jan 2016, 11:18
GMATGuruNY wrote: dk94588 wrote: Hello, this was on GMATprep, and I have had problems with this type of question before, but maybe you could help me solve it.
Tanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address?
A) 1/24 B) 1/8 C) 1/4 D) 1/3 E) 3/8 Let's call the envelopes E1, E2, E3 and E4. P(only E1 gets the correct letter): P(E1 gets the correct letter) = 1/4 (4 letters total, 1 of them correct) P(E2 gets the wrong letter) = 2/3 (3 letters left, 2 of them wrong) P(E3 gets the wrong letter) = 1/2 (2 letters left, 1 of them wrong) P(E4 gets the wrong letter) = 1/1 (1 letter left, and it must be wrong since we placed the correct letter in either E2 or E3) Since we need all of these events to happen, we multiply the fractions: 1/4 * 2/3 * 1/2 * 1/1 = 1/12. Since each envelope has the same probability of getting the correct letter and we have 4 envelopes total, we need to multiply by 4: 4 * 1/12 = 1/3. The correct answer is . I find your solution, the best among all. Thanks.
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Re: Tanya prepared 4 different letters to 4 different addresses. For each
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17 Jun 2017, 04:13
bagdbmba wrote: Tanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address?
A) 1/24 B) 1/8 C) 1/4 D) 1/3 E) 3/8 OPEN DISCUSSION OF THIS QUESTION IS HERE: tanyaprepared4differentletterstobesentto4different85167.html== Message from the GMAT Club Team == THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION. This discussion does not meet community quality standards. It has been retired. If you would like to discuss this question please repost it in the respective forum. Thank you! To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative  Verbal Please note  we may remove posts that do not follow our posting guidelines. Thank you.
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Re: Tanya prepared 4 different letters to 4 different addresses. For each
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Re: Tanya prepared 4 different letters to 4 different addresses. For each
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