Cards numbered $1$ to $30$ are put in a bag. A card is drawn at random from the bag. Find the probability that the number on the drawn card is not a perfect square number.

Cards bearing numbers $1, 3, 5, ........ 35$ are kept the bag. A card is drawn at random from the bag. Find the probability of getting a card bearing a prime number less than $15$.

Cards bearing numbers $1, 3, 5, ........ 35$ are kept the bag. A card is drawn at random from the bag. Find the probability of getting a card bearing a number divisible by $3$ and $5$.

If the answer is of the form $\frac{a}{b}$, then what is the value of $a$? 

A box contains cards bearing numbers $6$ to $70$. If one card is drawn at random from the box, find the probability that it bears a one-digit number.

A box contains cards bearing numbers $6$ to $70$. If one card is drawn at random from the box, find the probability that it bears a number divisible by $5$.

A box contains cards bearing numbers $6$ to $70$. If one card is drawn at random from the box, find the probability that it bears an odd number less than $30$.

A box contains cards bearing numbers $6$ to $70$. If one card is drawn at random from the box, find the probability that it bears an composite number between $50$ and $70$.

Cards marked with numbers $1, 3, 5, ..........., 101$ are placed in a bag and mixed thoroughly. A card is drawn at random from the bag. Find the probability that the number on the drawn card is less than $19$.

Cards marked with numbers $1, 3, 5, ..........., 101$ are placed in a bag and mixed thoroughly. A card is drawn at random from the bag. Find the probability that the number on the drawn card is a prime number less than $20$.

If the answer is of the form $\frac{a}{b}$, then what is the value of $a$?