If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the…

If the lengths of the sides of a triangle are decided by the three throws of a single fair die, then the probability that the triangle is of maximum area given that it is an isosceles triangle, is:
  1. 169
  2. 126
  3. 121
  4. 115

Solution

In a Δ sum of two sides should be greater then the third side

It is given that Δ is isosceles

∴ Total cases in which isosceles Δ will come is

1,1,1,2,2,3,2,2,1,2,2,2,3,3,4,3,3,1,3,3,2,3,3,3,3,3,5,4,4,1,4,4,2,4,4,3,4,4,4,4,4,5,4,4,6,5,5,1,5,5,2,5,5,3,5,5,4,5,5,5,5,5,6,6,6,1,6,6,2,6,6,3,6,6,4,6,6,5,6,6,6

Total cases =27×3−12=69

Favorable cases =1 

Probability = 169.

Asked in: JEE Main 2015 (11 Apr Online)

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