Question

If the numbers $1,2,3$ and $4$ are written separately on four slips of paper. The slips are put in a box and mixed thoroughly. A person draws two slips from the box, one after other, without replacement, then the odds against the number $1$ on the first slip is

Answer 1

The sample space of the experiment is
$S=\left\{\right(1,2),(1,3),(1,4),(2,1),(2,3),(2,4),(3,1),(3,2),(3,4),(4,1),(4,2),(4,3\left)\right\}$

Let $A$ be event for number $1$ on the first slip
$\therefore$ number of elements in $A$ is $3$
$P\left(A\right)=\frac{3}{12}=\frac{1}{4}$
$P\left(\overline{A}\right)=\frac{3}{4}$
$\therefore$ odds against $A=\frac{P\left(\overline{A}\right)}{P\left(A\right)}=\frac{\frac{3}{4}}{\frac{1}{4}}=3$