Why is tossing a coin considered to be a fair way of deciding which team should get the ball at the beginning of a football game?

$A$ box contains $12$ balls out of which $x$ are black. If one ball is drawn at random from the box,what is the probability that it will be a black ball?
If $6$ more black balls are put in the box,the probability of drawing a black ball is now double of what it was before. Find $x$.

$A$ die is thrown once. Find the probability of getting:
$(i)$ a prime number;
$(ii)$ a number lying between $2$ and $6$;
$(iii)$ an odd number.

Complete the following statements:
$(i)$ The sum of the probabilities of all the elementary events of an experiment is .......
$(ii)$ The probability of an event is greater than or equal to ....... and less than or equal to .......

$(i)$ $A$ 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?

$A$ game of chance consists of spinning an arrow which comes to rest pointing at one of the numbers $1, 2, 3, 4, 5, 6, 7, 8$ (see figure),and these are equally likely outcomes. What is the probability that it will point at:
$(i)$ $8?$
$(ii)$ an odd number?
$(iii)$ a number greater than $2?$
$(iv)$ a number less than $9?$