Odds of all possible outcomes in X tries?

D

Deadpool

New member
Joined
Feb 1, 2015
Messages
2
Let's say we have 30 possible outcomes. What are the odds I get all 30 possible outcomes at least once in 30 tries? What about in 60? 90?

What's the formula?
 
Deadpool said:
Let's say we have 30 possible outcomes. What are the odds I get all 30 possible outcomes at least once in 30 tries? What about in 60? 90? What's the formula?
Click to expand...
This is terribly difficult problem. It is known as Coupon collector's problem.
You may not think so once you read that page, but in fact the concepts are the same. If we had \(\displaystyle N\) different outcomes and made \(\displaystyle T=N\) trials the answer is easy: \(\displaystyle \dfrac{N!}{N^N}\), in this case \(\displaystyle N=30\).

The difficulty comes if \(\displaystyle T\) is the number of trials and \(\displaystyle T>N\), then that the mathematics on that website is used.
 
You must log in or register to reply here.
Top