Two balanced dice are rolled simultaneously. Then,the probability that the sum of numbers on the dice is $4$ is .........

At a fete, cards bearing numbers $1$ to $1000$, one number on one card, are put in a box. Each player selects one card at random and that card is not replaced. If the selected card has a perfect square greater than $500$, the player wins a prize. What is the probability that:
$(i)$ the first player wins a prize?
$(ii)$ the second player wins a prize, if the first has won?

$A$ coin is tossed two times. Find the probability of getting at most one head.

$A$ 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.

$A$ student attends a $50$ mark test. No negative marks are given in the test. Find the probability that he scores $30$ or $35$ marks.

Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is $2$.