Question

In each of the following experiments specify appropriate sample space.
$\left(i\right)$ A boy has a $1$ rupee coin, a $2$ rupee coin and a $5$ rupee coin in this pocket. He takes out two coins out of his pocket, one after the other.
$\left(ii\right)$ A person is noting down the number of accidents along a busy highway during a year.

Answer 1

$\left(i\right)$ Given: A boy has $1$ rupee coin, a $2$ rupee coin and a $5$ rupee coin in his pocket. He takes out two coins out of his pocket, one after the other.
Consider: $A$ denote a $1$ rupee coin, $B$ denotes a $2$ rupee coin and $C$ denotes a $5$ rupee coin.
He takes out two coins, one after the other.

$1^{st}$ coin	$2^{nd}$ coin
$A$	$B$
$A$	$C$
$B$	$A$
$B$	$C$
$C$	$A$
$C$	$B$

So, all possible outcomes are ($AB,AC,BA,BC,CA,CB$).
$\therefore$ The sample space $S=\{AB,AC,BA,BC,CA,CB\}$.

$\left(ii\right)$ Given : A person is noting down the number of accidents along a busy highway during a year.
It may be either $0$ accident, $1$ accident, $2$ accident, $3$ accident and so on.
(Accident can't be negative, fraction)
Thus, the Sample space $S=\{0,1,2,\mathrm{3...}\}$.