All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Probability
Probability of All of a Set (Posted on 2003-03-13) Difficulty: 5 of 5
Prove that the probability of occurrence of all of a given set of events A(1) through A(n) is equal to the sum of the individual probabilities minus the sum of the probabilities of all pairs of events, A(i) OR A(j) plus the sum of all triples of events, A(i) OR A(j) OR A(k), ..., plus (-1)^(n-1) times the n-tuple A(i) OR ... OR A(n).

Prove for the specific cases of n = 3 and n = 10, and the general case.

See The Solution Submitted by Charlie    
Rating: 3.2500 (4 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Explanation of a few terms | Comment 9 of 11 |
The Sum or Union of two sets A and B is denoted by (A + B) or (A U B) and is defined to be the set of all elements belonging to either A or B or both and the Product or Intersection of two sets A and B is denoted by 'AB' is deifined to be the set of all elements belonging to both A and B.

  Posted by Ravi Raja on 2003-03-17 04:03:33
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information