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14.Probability
hard
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
A
$\frac{1}{21}$
B
$\frac{1}{27}$
C
$\frac{1}{15}$
D
$\frac{1}{26}$
(JEE MAIN-2015)
Solution
Favourable case $= (6,6,6)$
Total case $= \{ (1,1,1)(2,2,1),(2,2,2),(2,2,3),(3,3,1)$
$ \ldots (3,3,5)(4,4,1) \ldots ..$
$(4,4,6)(5,5,1)….$
$(5,5,6)(6,6,1) \ldots (6,6,6)\} $
which satisfies condition $a + b > c$
Number of total case $= 27$
Probability $= \frac{1}{{27}}$
Standard 11
Mathematics
