A box contains $150$ bulbs out of which $15$ are defective. It is not possible to just look at a bulb and tell whether or not it is defective. One bulb is taken out at random from this box. Calculate the probability that the bulb taken out is a defective one.

Suppose the pen drawn in $\left(\mathrm{i}\right)$ is defective and is not replaced. Now one more pen is drawn at random from the rest. What is the probability that this pen is $\left(\mathrm{a}\right)$ defective ? $\left(\mathrm{b}\right)$not defective ?

A bag contains $100$ identical marble stones which are numbered from $1$ to $100$. If one stone is drawn at random from the bag, find the probability that it bears  a perfect square number.

A bag contains $100$ identical marble stones which are numbered from $1$ to $100$. If one stone is drawn at random from the bag, find the probability that it bears a number divisible by 4.

A bag contains $100$ identical marble stones which are numbered from $1$ to $100$. If one stone is drawn at random from the bag, find the probability that it bears a number divisible by 5.

A bag contains $100$ identical marble stones which are numbered from $1$ to $100$. If one stone is drawn at random from the bag, find the probability that it bears a number divisible by 4 or 5.

A bag contains $100$ identical marble stones which are numbered from $1$ to $100$. If one stone is drawn at random from the bag, find the probability that it bears a number divisible by 4 and 5.

A circle with diameter$20\mathrm{cm}$ is drawn somewhere on a rectangular piece of paper with length$40\mathrm{cm}$ and width$30\mathrm{cm}$. This paper is kept horizontal on table top and a dice, very small in size, is dropped on the rectangular paper without seeing towards it. If the dice falls and lands on the paper only, find the probability that it will fall and land inside the circle. [Use, $\mathrm{\pi }=\frac{22}{7}$]