Source: Official Guide Revised GRE 2nd Ed. Part 9; Section 6; #25

3

Eight points are equally spaced on a circle

Eight points are equally spaced on a circle. If 4 of the 8 points are to be chosen at random, what is the probability that a quadrilateral having the 4 points chosen as vertices will be a square? 1/70, 1/35, 1,7, 1/4, 1/2

2 Explanations

10

Eric Kuzmenko

You can also do this: 1×(3÷7)×(2÷6)×(1÷5)

Explanation:
probability of choosing the first vertex is 1
TIMES
probability of choosing one of corresponding vertices of the square is then 3/7
TIMES
probability of choosing another (3rd) vertex is 2/6
TIMES
probability of choosing the last (4th) vertex is 1/5

You don't multiply this by two (although there are two different squares you can make) because the first vertex you've picked as immediately limited you to one of the squares.

Aug 12, 2014 • Comment

3

Gravatar Chris Lele, Magoosh Tutor

Dec 8, 2012 • Comment

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