Question

A game has $8$ triangles of which $6$ are blue and rest are green, $12$ rectangles of which $3$ are green and rest are blue, and $10$ rhombuses of which $3$ are blue rest are green. One piece is lost a random. Find the probability that it is a green triangle.

Answer 1

We know that ,

$ProbabilityP\left(E\right)=\frac{Totalnumberoffavorableeventn\left(E\right)}{Totalnumberofpossibleoutcomen\left(S\right)}$

Now there are,

$8$ triangle$=6$ blue$+2$ green

$10$ rhombus$=3$ blue$+7$ green

$12$ rectangle $=9$ blue$=3$ green

on adding

total number of possible outcome $n\left(S\right)=30$

Now,

Probability of getting green triangle

there are $2$ green triangle

So,

$n\left(E\right)=2$

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

$P\left(E\right)=\frac{2}{30}$

Hence, the outcome is

$P\left(E\right)=\frac{1}{15}$