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

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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