$A$ circle with radius $7 \, cm$ is drawn at the centre of a rectangle $28 \, cm$ long and $22 \, cm$ broad. Find the probability that a ball hitting the rectangle hits the circle.

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 $18$?

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

$(i)$ $A$ lot of $20$ bulbs contains $4$ defective ones. One bulb is drawn at random from the lot. What is the probability that this bulb is defective?
$(ii)$ Suppose the bulb drawn in $(i)$ is not defective and is not replaced. Now one bulb is drawn at random from the rest. What is the probability that this bulb is not defective?

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 $\frac{1}{2}$.

$A$ 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?