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A certain board game consists of a circular path of 100 spaces colored
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Updated on: 16 Aug 2015, 12:32
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A certain board game consists of a circular path of 100 spaces colored in a repeating pattern of black, yellow, green, red and blue. what is the probability that, in a random selection of seven consecutive spaces, 2 of the spaces are blue? A. 2/25 B. 1/7 C. 1/5 D. 2/7 E. 2/5
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Originally posted by akriti13 on 07 Mar 2011, 01:02.
Last edited by Bunuel on 16 Aug 2015, 12:32, edited 1 time in total.
Renamed the topic and edited the question.




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Re: A certain board game consists of a circular path of 100 spaces colored
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07 Mar 2011, 02:49
Moved to PS subforum. akriti13 wrote: a certain board game consists of a circular path of 100 spaces colored in a repeating pattern of black, yellow, green, red and blue. what is the probability that, in a random selection of seven consecutive spaces, 2 of the spaces are blue?
a)2/25 b)1/7 c)1/5 d)2/7 e)2/5 We have a pattern of 5 colors: black  yellow  green  red  blue. To have 2 blue spaces in a string of 7 spaces the starting space must be either blue or red (in I case: first and sixth spaces will be blue and in the II case: second and seventh spaces will be blue). The probability that the starting space will be either blue or red is 2/5. Answer: E. P.S. Please post PS questions in the PS subforum: gmatproblemsolvingps140/and DS questions in the DS subforum: gmatdatasufficiencyds141/ No posting of PS/DS questions is allowed in the main Math forum.
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Re: A certain board game consists of a circular path of 100 spaces colored
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07 Mar 2011, 03:05
Ans: "E" There are 100 possible ways to select 7 consecutive spaces. 17 28 39 410 . . 98104 99105 100106 Let's fix the first colored space as Black; Representing Black as K and blue as B. KYGRBKYGRBKYGRBKYGRB... 20 SUCH GROUPS How to get 2 blues. KYG [R {BKYGRB ]K }YGRBKYGRB If the starting space is Red and last space Blue; positions will be; 4,9,14,19,....94,99= count 20 OR If the starting space is Blue and last space Black; positions will be; 5,10,15,20...95,100= count 20 20+20=40 There are 40 favorable ways. P=40/100=2/5 Ans: "E"
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Re: A certain board game consists of a circular path of 100 spaces colored
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07 Mar 2011, 03:14
fluke wrote: Ans: "E"
There are 100 possible ways to select 7 consecutive spaces. 17 28 39 410 . . 98104 99105 100106
Let's fix the first colored space as Black; Representing Black as K and blue as B. KYGRBKYGRBKYGRBKYGRB... 20 SUCH GROUPS
How to get 2 blues. KYG[R{BKYGRB]K}YGRBKYGRB
If the starting space is Red and last space Blue; positions will be; 4,9,14,19,....94,99= count 20 OR If the starting space is Blue and last space Black; positions will be; 5,10,15,20...95,100= count 20
20+20=40
There are 40 favorable ways.
P=40/100=2/5
Ans: "E" It's simpler then this. The question basically asks the probability of the first space being either blue or red and as there are total of 5 colors then the probability is simply 2/5.
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Re: A certain board game consists of a circular path of 100 spaces colored
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07 Mar 2011, 03:16
fluke Pls see this reasoning. Can I rephrase the question as?
What is the probability of getting 5n or 5n1 in 100 numbers ?
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Re: A certain board game consists of a circular path of 100 spaces colored
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07 Mar 2011, 03:21
Bunuel wrote: It's simpler then this. The question basically asks the probability of the first space being either blue or red and as there are total of 5 colors then the probability is simply 2/5. gmat1220 wrote: fluke Pls see this reasoning. Can I rephrase the question as?
What is the probability of getting 5n or 5n1 in 100 numbers ?
cheers
Exactly!! I realized that after seeing your posts. Thanks and kudos to both.
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Re: A certain board game consists of a circular path of 100 spaces colored
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07 Mar 2011, 03:55
fluke, Bunuel your explanations are awesome.



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Re: A certain board game consists of a circular path of 100 spaces colored
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07 Mar 2011, 09:44
Hi guys, Thanks for the quick reply. Bunuel: point noted about the posting rules, sorry.



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Re: A certain board game consists of a circular path of 100 spaces colored
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07 Mar 2011, 21:11
My take : The pattern is : black, yellow, green, red, blue  black, yellow, green, red, blue  black, yellow, green, red, blue The desired pattern can happen only in  red, blue, black, yellow, green, red, blue or in  blue, black, yellow, green, red, blue, black Total ways of choosing 7 consecutive = 5 after which the patterns repeat : black, yellow, green, red, blue, black, yellow yellow, green, red, blue, black, yellow, green green, red, blue, black, yellow, green, red red, blue, black, yellow, green, red, blue blue, black, yellow, green, red, blue, black So Prob = 2/5 Answer is E.
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Re: A certain board game consists of a circular path of 100 spaces colored
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18 Jul 2017, 00:09
Bunuel wrote: Moved to PS subforum. akriti13 wrote: a certain board game consists of a circular path of 100 spaces colored in a repeating pattern of black, yellow, green, red and blue. what is the probability that, in a random selection of seven consecutive spaces, 2 of the spaces are blue?
a)2/25 b)1/7 c)1/5 d)2/7 e)2/5 We have a pattern of 5 colors: black  yellow  green  red  blue. To have 2 blue spaces in a string of 7 spaces the starting space must be either blue or red (in I case: first and sixth spaces will be blue and in the II case: second and seventh spaces will be blue). The probability that the starting space will be either blue or red is 2/5. Answer: E. P.S. Please post PS questions in the PS subforum: http://gmatclub.com/forum/gmatproblemsolvingps140/and DS questions in the DS subforum: http://gmatclub.com/forum/gmatdatasufficiencyds141/ No posting of PS/DS questions is allowed in the main Math forum. I do not think that 2/5 is the answer here. It would have been If there were infinite number or a very large number of consecutive repetitions here. Since we have only 100 numbers, we have to count the number of times each of these patterns occurs, and also the number of ways in which we can select 7 consecutive numbers here, I hope I'm not confusing you. So when I counted, I found that there are a total of 1007+1 = 94 ways in which we can select 7 consecutive patterns. Now, we know that every color occurs 20 times, as it's a recurring pattern of 5 colors. But, we cannot select 7 consecutive numbers starting from any of the last 6 numbers, and they have to removed from counting the total number of patterns that we can select. From this I found that.. BY 19 YG 19 GR 19 Rb 19 bB 18 Total = 94 Where BY represents the pattern of 7 colors that starts from Black and ends in Y. B = Black and b = Blue. Only in the last two patterns will there be two blues. Final probability 37/94 Not listed. What's wrong! Experts, a little help please.
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Re: A certain board game consists of a circular path of 100 spaces colored
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18 Jul 2017, 00:13
ShashankDave wrote: Bunuel wrote: Moved to PS subforum. akriti13 wrote: a certain board game consists of a circular path of 100 spaces colored in a repeating pattern of black, yellow, green, red and blue. what is the probability that, in a random selection of seven consecutive spaces, 2 of the spaces are blue?
a)2/25 b)1/7 c)1/5 d)2/7 e)2/5 We have a pattern of 5 colors: black  yellow  green  red  blue. To have 2 blue spaces in a string of 7 spaces the starting space must be either blue or red (in I case: first and sixth spaces will be blue and in the II case: second and seventh spaces will be blue). The probability that the starting space will be either blue or red is 2/5. Answer: E. P.S. Please post PS questions in the PS subforum: http://gmatclub.com/forum/gmatproblemsolvingps140/and DS questions in the DS subforum: http://gmatclub.com/forum/gmatdatasufficiencyds141/ No posting of PS/DS questions is allowed in the main Math forum. I do not think that 2/5 is the answer here. It would have been If there were infinite number or a very large number of consecutive repetitions here. Since we have only 100 numbers, we have to count the number of times each of these patterns occurs, and also the number of ways in which we can select 7 consecutive numbers here, I hope I'm not confusing you. So when I counted, I found that there are a total of 1007+1 = 94 ways in which we can select 7 consecutive patterns. Now, we know that every color occurs 20 times, as it's a recurring pattern of 5 colors. But, we cannot select 7 consecutive numbers starting from any of the last 6 numbers, and they have to removed from counting the total number of patterns that we can select. From this I found that.. BY 19 YG 19 GR 19 Rb 19 bB 18 Total = 94 Where BY represents the pattern of 7 colors that starts from Black and ends in Y. B = Black and b = Blue. Only in the last two patterns will there be two blues. Final probability 37/94 Not listed. What's wrong! Experts, a little help please. 2/5 is correct. The question basically asks the probability of the first space being either blue or red and as there are total of 5 colors then the probability is simply 2/5.
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Re: A certain board game consists of a circular path of 100 spaces colored
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