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 triangle.

Answer 1

We know that,

Probability$P\left(E\right)=\frac{totalnumberoffavorableeventn\left(E\right)}{totalnumberofpossibleoutcomen\left(S\right)}$

Now there are,

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

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

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

on adding,

Total numbere of possible outcome $n\left(s\right)=30$

now,

probability of getting triangle

there are $3$triangle

So,

$n\left(E\right)=8$

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

$P\left(E\right)=\frac{8}{30}$

Hence, the outcome is

$P\left(E\right)=\frac{4}{15}$