- Related Questions & Answers
- How to read the data from a properties file in Java?
- C++ Program for Dijkstra’s shortest path algorithm?
- Ways to paint N paintings such that adjacent paintings don’t have same colors in C programming
- Find the k most frequent words from data set in Python
- Inbuilt Data Structures in Python
- Get data from sessionStorage in JavaScript?
- How to append data to a file in Java?
- Program to build DFA that starts and ends with ‘a’ from the input (a, b)
- When a lot of changes are required in data, which one you choose String or StringBuffer in java?
- How to open a website in Android’s web browser from any application?
- How to pass data between activities in Android?
- The Maximum Data Rate of a Channel
- Prim’s (Minimum Spanning Tree) MST Algorithm
- Kruskal’s (Minimum Spanning Tree) MST Algorithm
- How to compress and un-compress the data of a file in Java?

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

In probability theory, according to Boole's inequality, also denoted as the union bound, for any finite or countable set of events, the probability that at least one of the events happens is no higher than the sum of the probabilities of the individual events.

In mathematics, the probability theory is denoted as an important branch that studies about the probabilities of the random event. The probability is denoted as the measurement of chances of happening an event which is an outcome of an experiment.

**For Example** − tossing a coin is denoted as an experiment and getting head or tail is denoted as an event. Ideally, there are50%-50% chances, that is 1/2-1/2 probability of obtaining either a head or a tail.

There are so many important concepts in probability theory.

Boole's inequality is one of them.

The union bound or Boole's inequality is applicable when we need to show that the probability of the union of some events is smaller than some value.

Remember that for any two events C and D we have

P(C ∪ D) = P(C) + P(D) − P(C ∩ D) ≤ P(C) + P(D).

Similarly, for three events C, D, and E, we can write

P(C ∪ D ∪ E) = P((C ∪ D) ∪ E) ≤ P(C ∪ D) + P(E) ≤ P(C) + P(D) + P(E).

Advertisements