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A certain board game consists of a circular path of 100 spaces colored

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akriti13
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A certain board game consists of a circular path of 100 spaces colored [#permalink] New post   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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E

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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Bunuel
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Re: A certain board game consists of a circular path of 100 spaces colored [#permalink] New post   07 Mar 2011, 02:49
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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: gmat-problem-solving-ps-140/
and DS questions in the DS subforum: gmat-data-sufficiency-ds-141/ No posting of PS/DS questions is allowed in the main Math forum.
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fluke
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Re: A certain board game consists of a circular path of 100 spaces colored [#permalink] New post   07 Mar 2011, 03:05
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Ans: "E"

There are 100 possible ways to select 7 consecutive spaces.
1-7
2-8
3-9
4-10
.
.
98-104
99-105
100-106

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 [#permalink] New post   07 Mar 2011, 03:14
Expert Reply
fluke wrote:
Ans: "E"

There are 100 possible ways to select 7 consecutive spaces.
1-7
2-8
3-9
4-10
.
.
98-104
99-105
100-106

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 [#permalink] New post   07 Mar 2011, 03:16
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fluke
Pls see this reasoning. Can I rephrase the question as?

What is the probability of getting 5n or 5n-1 in 100 numbers ?

cheers
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Re: A certain board game consists of a circular path of 100 spaces colored [#permalink] New post   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 5n-1 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 [#permalink] New post   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 [#permalink] New post   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 [#permalink] New post   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 [#permalink] New post   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: https://gmatclub.com/forum/gmat-problem-solving-ps-140/
and DS questions in the DS subforum: https://gmatclub.com/forum/gmat-data-sufficiency-ds-141/ 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 100-7+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..

B--Y 19
Y--G 19
G--R 19
R--b 19
b--B 18

Total = 94

Where B--Y 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 [#permalink] New post   18 Jul 2017, 00:13
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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: https://gmatclub.com/forum/gmat-problem-solving-ps-140/
and DS questions in the DS subforum: https://gmatclub.com/forum/gmat-data-sufficiency-ds-141/ 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 100-7+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..

B--Y 19
Y--G 19
G--R 19
R--b 19
b--B 18

Total = 94

Where B--Y 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 [#permalink]
18 Jul 2017, 00:13
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