Cards with numbers $2$ to $101$ are placed in a box. $A$ card is selected at random. Find the probability that the card has
$(i)$ an even number
$(ii)$ a square number

Which of the following arguments are correct and which are not correct? Give reasons for your answer.
$(i)$ If two coins are tossed simultaneously,there are three possible outcomes - two heads,two tails,or one of each. Therefore,for each of these outcomes,the probability is $\frac{1}{3}$.
$(ii)$ If a die is thrown,there are two possible outcomes - an odd number or an even number. Therefore,the probability of getting an odd number is $\frac{1}{2}$.

$A$ lot consists of $48$ mobile phones of which $42$ are good,$3$ have only minor defects,and $3$ have major defects. Varnika will buy a phone if it is good,but the trader will only buy a mobile if it has no major defect. One phone is selected at random from the lot. What is the probability that it is
$(i)$ acceptable to Varnika?
$(ii)$ acceptable to the trader?

$A$ box contains $90$ discs which are numbered from $1$ to $90$. If one disc is drawn at random from the box, find the probability that it bears:
$(i)$ a two-digit number
$(ii)$ a perfect square number
$(iii)$ a number divisible by $5$.

Box $A$ contains $25$ slips of which $19$ are marked $Rs. 1$ and others are marked $Rs. 5$ each. Box $B$ contains $50$ slips of which $45$ are marked $Rs. 1$ each and others are marked $Rs. 13$ each. Slips of both boxes are poured into a third box and reshuffled. $A$ slip is drawn at random. What is the probability that it is marked other than $Rs. 1$?

Two unbiased dice are thrown once. Write all the possible outcomes of this experiment. What is the probability that the sum of numbers on two dice is a factor of $18$?