In a lottery, n tickets are sold and there is only one prize. If you purchase m tickets, what is the probability that you do NOT win a prize?
If there are n tickets and you have m tickets, this means the chance of winning a prize is:
$$P(Prize)=\frac{m}{n}$$
hence the probability of NOT winning a prize would be its complement ie 1 – P(prize)
$$P(Not\,Prize)=1-\frac{m}{n}$$