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:

Step-by-step 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 − 1