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A bag contains balls numbered $2$ to $91$ such that each ball bears a different number. A ball is drawn at random from the bag. Find the probability that (i) it bears a $2$-digit number (ii) it bears a multiple of $1$.
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Total possible outcomes = $90$
(i) Number of favourable outcomes for a $2$-digit number = $82$
$P(2\text{-digit number}) = \frac{82}{90}$ or $\frac{41}{45}$
(ii) Number of favourable outcomes for multiple of $1 = 90$
$P(\text{a number multiple of } 1) = \frac{90}{90}$ or $1$
(i) Number of favourable outcomes for a $2$-digit number = $82$
$P(2\text{-digit number}) = \frac{82}{90}$ or $\frac{41}{45}$
(ii) Number of favourable outcomes for multiple of $1 = 90$
$P(\text{a number multiple of } 1) = \frac{90}{90}$ or $1$