# Inverse Probability — Bayes Theorem — Conditional Probability — Data Science

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In this article, we are going to see about **Inverse Probability** or **Reverse probability** and how it is related to the **Bayes Theorem**.

Recently I have attended a **technical interview for a Data Science Internship** and the interviewer asked “**What is Inverse Probability ?**” to me. At that time I don’t even hear about this word. Later I searched about it on the internet and came with this article to explain every one. Let’s see what it is…

# What is Inverse Probability?

**Inverse Probability **or** Reverse Probability **is the **probability** of an entity that is not taken into account. In other words, more technically, the **probability** distribution of an unobserved entity.

The Inverse Probability can be found with **Conditional Probability**.

# Use Case

Let us consider two students in a class. Student 1 is having a Green bag (G) and Student 2 is having a Blue bag (B).

Each bag consists of a countable number of notebooks.

- The green bag consists of 3 short notebooks (S) and 9 long notebooks (L).
- The blue bag consists of 5 short notebooks and (S) 6 long notebook (L).

Now we are going to **find the probability or chance of getting a short notebook from the green bag given all the short notebooks.**

Probability of getting a notebook from green bag,

`P ( Green Bag ) = 12 / 23`

Probability of the blue bag

`P ( Blue Bag ) = 11 / 23`

Our goal is to find the probability of getting a short notebook from the Green bag given all the short notebooks which is P ( Green Bag|Short Notebook ).

Probability of getting a short notebook,

`P( Short Notebook ) = 8 / (12 + 11) = 8 / 23`

Probability of taking a short notebook from the green bag,

`P( Short Notebook | Green Bag ) = 3 / 12`

Hence the probability of taking a short notebook from the green bag given all the short notebooks will be given as ,

P( Green bag | Short Notebooks) = ((3 / 12) * (12 / 23)) / (8 / 23)P ( Green bag | Short Notebooks ) = ( 3/ 23 ) / ( 8/ 23 )P ( Green bag | Short Notebooks ) = 3 / 8 (or) 0.375

Hence, there is approximately 37.5% chance taking a short notebook from the green bag given all the short notebooks

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