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 smaller than $2$?

At a toy shop,there are $10$ toys in a box of which $3$ toys are defective. $A$ customer would purchase a non-defective toy only. The probability that a toy selected at random from the box is purchased by the customer is ..............

Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on the dice is
$(i)$ $7 ?$
$(ii)$ a prime number?
$(iii)$ $1 ?$

$A$ card is drawn at random from a well-shuffled pack of $52$ cards. Find the probability that the card drawn is a king of a black suit.

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 $4$?

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?