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# What is the probability of randomly selecting one of the shortest diag

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Math Expert
Joined: 02 Sep 2009
Posts: 64318
What is the probability of randomly selecting one of the shortest diag  [#permalink]

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07 Sep 2016, 03:41
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65% (hard)

Question Stats:

57% (01:54) correct 43% (01:35) wrong based on 136 sessions

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What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular hexagon?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 7/9

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Joined: 23 Apr 2015
Posts: 266
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Re: What is the probability of randomly selecting one of the shortest diag  [#permalink]

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10 Sep 2016, 23:15
1
Bunuel wrote:
What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular hexagon?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 7/9

A regular hexagon has 3 diagonals in which 2 are of same length and shorter than the other.
so probability = $$\frac{2}{3}$$ Answer is D
Math Expert
Joined: 02 Aug 2009
Posts: 8634
Re: What is the probability of randomly selecting one of the shortest diag  [#permalink]

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07 Sep 2016, 04:16
Bunuel wrote:
What is the probability of randomly selecting one of the shortest diagonals from all the diagonals of a regular hexagon?

A. 1/4
B. 1/3
C. 1/2
D. 2/3
E. 7/9

Hi,
Two ways...
1) just imagine any any vertex or a corner....
It has two vertices on sides, which do not make a diagonal but a side..
So remaining 3 vertices make diagonals... only the opposite vertex will make largest diagonal and other TWO smaller ones..
So prob =2/(2+1)=2/3

2) each vertex will make the largest diagonal, so 6/2=3..
Total diagonals=6C2-number of sides= 5*6/2 - 6=15-6=9..
Ans (9-3)/9=2/3

D
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Re: What is the probability of randomly selecting one of the shortest diag  [#permalink]

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14 Aug 2017, 09:07
1
The number of diagonals of a polygon is given in the formula: n(n-3)/2 , where n is the number of sides. In the case of the hexagon, the n=6.

A regular hexagon has diagonals: 6(6-3)/2=9 diagonals

Of these 9, 6 are smaller diagonals and three are longer diagonals.

That's a 6/9 = 2/3 chance of randomly picking a shorter diagonal.
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Re: What is the probability of randomly selecting one of the shortest diag  [#permalink]

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23 Apr 2020, 19:08
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Re: What is the probability of randomly selecting one of the shortest diag   [#permalink] 23 Apr 2020, 19:08