JEE Main 2015 · 11 Apr · Shift 1 · Mathematics Q86

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MathematicsSingle correct+4 / -1Question 86 of 90

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 :

\dfrac1{26}

\dfrac1{27}

\dfrac1{21}

\dfrac1{15}

Answer and worked solution

Official answer: B

The key counts unordered side-sets as equally likely.

Equilateral sets: 6.
Other isosceles sets $(x,x,y)$ with $y<2x$ , $y\ne x$ : 0, 2, 4, 5, 5 and 5 for $x=1,\dots,6$ , i.e. 21.

That is 27 isosceles sets. The largest area is the 6-6-6 triangle, so the probability is $\frac1{27}$ .

Topics:Conditional probability Fundamental principle of counting

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JEE Main 2015 · 11 Apr · Shift 1, Mathematics question 86