Question

A box contains tickets of two different colours: blue and green. There are $3$ blue tickets. If two tickets are to be drawn together at random from the box, the probability that there is one ticket of each colour is $\frac{1}{2}$. Possible number of green tickets in box can be

• A. $1$
• B. $3$
• C. $6$
• D. $8$

Answer 1

Answer: (A), (C)

The correct options are
A $1$
C $6$

Let $Green\to g,blue\to 3$

$\frac{1}{2}=\frac{{3C}_1.g{C}_1}{{}^{g+3}{C}_2}$

$\Rightarrow \frac{(g+3)(g+2)}{2}=3.g.2$
$\Rightarrow g^2+5g+6=12g\Rightarrow g^2-7g+6=0$
$\Rightarrow g=1$ or $6$