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title: Conditional Probability
---
## Conditional Probability

A conditional probability is the probability of an event, given some other event has already occurred. So, for example, the conditional probability of an event **A** is the probability that the event will occur given that an event **B** has already occurred. This probability is denoted as `P(A|B)`.

The conditional probability of an event **A** given that an event **B** has occurred is written as follows:

![conditional probability formula](https://pbiswas101.files.wordpress.com/2018/10/conditional-probability.png?w=450) **as long as P(B) > 0**

**NOTE** - In the case where events **A** and **B** are independent (where event **B** has no effect on the probability of event **A**), the conditional probability of event **A** given event **B** is simply the probability of event **A**, i.e. `P(A)`.

### Resources
- [Conditional Probability - Wikipedia](https://en.wikipedia.org/wiki/Conditional_probability)
- [MIT OpenCourseWare - Youtube](https://www.youtube.com/watch?v=JGeTcRfKgBo)