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?
You have to buy at least
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
Thus, the minimum integer that meets
[What is the point?]
The concept I applied to this question is called 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.
If you solve this from the front, you need to consider three cases.
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