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A bag contains cards which are numbered from $5$ to $100$ such that each card bears a different number. A card is drawn at random. Find the probability that number on the card is (i) a perfect square (ii) a $2$-digit number
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Total possible outcomes = $96$
(i) Number of favourable outcomes for perfect square = $8$
$P(\text{perfect square}) = \frac{8}{96}$ or $\frac{1}{12}$
(ii) Number of favourable outcomes for a $2$-digit number = $90$
$P(\text{a } 2\text{-digit number}) = \frac{90}{96}$ or $\frac{15}{16}$
(i) Number of favourable outcomes for perfect square = $8$
$P(\text{perfect square}) = \frac{8}{96}$ or $\frac{1}{12}$
(ii) Number of favourable outcomes for a $2$-digit number = $90$
$P(\text{a } 2\text{-digit number}) = \frac{90}{96}$ or $\frac{15}{16}$