Complicated math probability problem! 10 points
Favorites|Homepage
Subscriptions | sitemap
HOME > Mathematics > Complicated math probability problem! 10 points

Complicated math probability problem! 10 points

[From: ] [author: ] [Date: 11-08-25] [Hit: ]
...So youll never have a 50 percent chance if the numbers are truly random.......
If each person randomly gets a number between 1 and 10
then how many many people do you need together for there to be more than a 50 percent chance for two of them to have the same number.

Show how you did it please!

-
Consider the probability that no two have the same number.
If there is one person, the probability is 10/10 = 1.
If there are two people, the probability is 10/10 * 9/10.
... three people, the probability is 10/10 * 9/10 * 8/10
and so on.

So the question becomes this: what is the smallest number k such that
(10 * 9 * ... * (10-k+1)) / 10^k < 1/2.

I don't know of a good way to do this, but if you start testing them, you'll find that
(10 * 9 * 8 * 7) / 10^4 = 0.504
(10 * 9 * 8 * 7 * 6) / 10^5 = 0.3024

Therefore the answer is 5 people. Note, though, that with 5 people the probability that some two have the same number is given by
1 - 0.3024 = 0.6976

-
Well if its random then every 10 people should statistically have a number between 1 and 10....
So you'll never have a 50 percent chance if the numbers are truly random.

-
Ask you parents or something
1
keywords: Complicated,problem,10,points,math,probability,Complicated math probability problem! 10 points
New
Hot
© 2008-2010 http://www.science-mathematics.com . Program by zplan cms. Theme by wukong .