# A lottery claims that 10% of tickets win a prize. How many tickets should you purchase to be more than 50% sure of winning a prize?

##### 1 Answer

You have to buy at least

#### Explanation:

Let

In this lottery tickets, the probability for NOT winning a prize is

If you want more than

the number of tickets you have to buy

Put

Thus, the minimum integer that meets

[What is the point?]

The concept I applied to this question is called **complementary event**.

https://en.wikipedia.org/wiki/Complementary_event

This idea is useful to evaluate the probability for having at least one event.

Consider a simpler case and you will notice the convenience.

[Example]

If you solve this from the front, you need to consider three cases.

(a) three

(b) two

(c) a

It will be complicated. Insted, you can solve it from the back door.

(1) If a dice is rolled, the probability of **not** having a

(2) When three dices are rolled, they are independent. So the probability of having no

(3) Having at least one 6 is