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a ps fro, gmat club

by diebeatsthegmat » Tue Mar 08, 2011 1:30 pm
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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by GMATGuruNY » Tue Mar 08, 2011 2:10 pm
diebeatsthegmat 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
P = (good outcomes)/(total possible outcomes)

Total possible outcomes = 5. (The 7 spaces could start with black, yellow, green, red or blue.)

To get 2 blues, the 7 spaces must start either with red (red, blue, black, yellow, green, red, blue) or with blue (blue, black, yellow, green, red, blue, black).
Thus, good outcomes = 2.

P(2 blue) = 2/5.

The correct answer is E.
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by manpsingh87 » Fri Mar 18, 2011 12:02 am
diebeatsthegmat 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
selection can begin from any of the five colors as follows:

1)black,yellow,green,red,blue,black,yellow
2) yellow,green,red,blue,black,yellow,green
3)green,red,blue,black,yellow,green,red.
4)red,blue,black,yellow,green,red,blue.
5)blue,black,yellow,green,red,blue,black.

out of the 5 possible outcomes only two are favorables i.e. option 4 and 5 hence required probability is 2/5 i.e. e
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