Mathematics - Probability Question with Solution | TestHub

In a$\mathrm{\Delta }$sum of two sides should be greater then the third side

It is given that$\mathrm{\Delta }$is isosceles

$\therefore$Total cases in which isosceles$\mathrm{\Delta }$will come is

$\left(1,1,1\right),\left(2,2,3\right),\left(2,2,1\right),\left(2,2,2\right),\left(3,3,4\right),\left(3,3,1\right),\left(3,3,2\right),\left(3,3,3\right),\left(3,3,5\right),\left(4,4,1\right),\left(4,4,2\right),\left(4,4,3\right),\left(4,4,4\right),\left(4,4,5\right),\left(4,4,6\right),\left(5,5,1\right),\left(5,5,2\right),\left(5,5,3\right),\left(5,5,4\right),\left(5,5,5\right),\left(5,5,6\right),\left(6,6,1\right),\left(6,6,2\right),\left(6,6,3\right),\left(6,6,4\right),\left(6,6,5\right),\left(6,6,6\right)$

Total cases$=27\times 3-12=69$

Favorable cases$=1$

Probability =$\frac{1}{69}.$