Two balanced dice are rolled. Find the probability that the sum of numbers on two dice lies between $5$ and $9$.

$A$ box contains $5$ red marbles,$8$ white marbles and $4$ green marbles. One marble is taken out of the box at random. What is the probability that the marble taken out will be
$(i)$ red?
$(ii)$ white?
$(iii)$ not green?

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 $18$?

$A$ 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?

$A$ carton of $24$ bulbs contains $6$ defective bulbs. One bulb is drawn at random. What is the probability that the bulb is not defective? If the bulb selected is defective and it is not replaced, and a second bulb is selected at random from the rest, what is the probability that the second bulb is defective?

$A$ bag contains $3$ red balls and $5$ black balls. $A$ ball is drawn at random from the bag. What is the probability that the ball drawn is
$(i)$ red?
$(ii)$ not red?