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  • Help me solve this 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 :

 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 :

  • Option 1) (1/26)
  • Option 2) (1/27)
  • Option 3) (1/21)
  • Option 4) (1/15)
 

Answers (1)

As we learnt in 

Probability of occurrence of an event -

Let S be the sample space then the probability of occurrence of an event E is denoted by P(E) and it is defined as 

P\left ( E \right )=\frac{n\left ( E \right )}{n\left ( S \right )}

P\left ( E \right )\leq 1

P(E)=\lim_{n\rightarrow\infty}\left(\frac{r}{n} \right )

 

 

- wherein

Where n repeated experiment and E occurs r times.

 

Consider 21 cases of isosceles triangle each case occuring thrice

(2,2,1) (2,2,3) (3,3,1) (3,3,2) (3,3,4)---------------------(6,6,5). Out\ of\ which\ (66,6)

Hence  required probability = \frac{1}{21}

If we consider equilateral triangle, there are 63 occurences of non-equilateral triangle and 6 occurences of equilateral triangle.

Required probability =\frac{1}{27}

 


Option 1)

\frac{1}{26}

This is incorrect option

Option 2)

\frac{1}{27}

This is correct option

Option 3)

\frac{1}{21}

This is incorrect option

Option 4)

\frac{1}{15}

This is incorrect option

Posted by

Vakul

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