Question

A box contains $10$ green, $20$ red, $30$ black and $40$ orange marble. One marble is drawn from the box at random. The probability that marble is neither green nor orange is:

• A. $\frac{1}{2}$
• B. $\frac{7}{10}$
• C. $\frac{3}{5}$
• D. $\frac{1}{3}$

Answer 1

The correct option is A $\frac{1}{2}$

Let's denote green coloured marbles with $G$, red coloured with $R$, black coloured with $B$ and orange with $O.$
$\therefore P\left(G\right)=0.1,P\left(R\right)=0.2,P\left(B\right)=0.3,P\left(O\right)=0.4$
Let the desired event be denoted by $E.$
$\Rightarrow P\left(E\right)=P(G^c\cap O^c)=1-P(G\cup O)=1-P\left(G\right)-P\left(O\right)+P(G\cap O)$
$\Rightarrow P(G^c\cap O^c)=1-0.1-0.4+0$
$P(G\cap O)=0$ because one marble can't be of two different colour as per the question.
$\therefore P(G^c\cap O^c)=\frac{1}{2}$