Unconditional Probability Using Total Probability Rule

As we learned earlier, the total probability rule determines the unconditional probability of an event in terms of probabilities conditional on scenarios.

P(A) = P(A | S1)P(S1) + P(A | S2)P(S2) + … + P(A | Sn)P(Sn)

Where the scenarios S1, S2, …Sn are mutually exclusive and exhaustive.

Let’s take one more example of the Total Probability Rule.

An analyst is assessing the performance of a stock under different scenarios. He comes up with the following probabilities.

State of EconomyProbability of Economic StateStock PerformanceProbability
No recession P(RC)0.60Rise P(SR | RC)0.70
Fall P(SRC | RC)0.30
Recession P(R)0.40Rise P(SR | R)0.20
Fall P(SRC | R)0.80

Question 1

Based on the above data, what is the total probability of a stock rise? We need to find the unconditional probability of a stock rise under all scenarios.

P(SR) = P(SR | RC) P(RC) + P(SR | R) P(R)

\= 0.70*0.60 + 0.20*0.40 = 0.5

Question 2

What is the joint probability of having a recession and at the same time having a stock price fall?

P(R and SRC) = P(SRC | R)x P(R) = 0.8*0.4 = 0.32

Related Downloads

Related Quizzes

Probablity Concepts

Data Science in Finance: 9-Book Bundle

Data Science in Finance Book Bundle

Master R and Python for financial data science with our comprehensive bundle of 9 ebooks.

What's Included:

  • Getting Started with R
  • R Programming for Data Science
  • Data Visualization with R
  • Financial Time Series Analysis with R
  • Quantitative Trading Strategies with R
  • Derivatives with R
  • Credit Risk Modelling With R
  • Python for Data Science
  • Machine Learning in Finance using Python

Each book includes PDFs, explanations, instructions, data files, and R code for all examples.

Get the Bundle for $39 (Regular $57)
JOIN 30,000 DATA PROFESSIONALS

Free Guides - Getting Started with R and Python

Enter your name and email address below and we will email you the guides for R programming and Python.

Data Science in Finance: 9-Book Bundle

Data Science in Finance Book Bundle

Master R and Python for financial data science with our comprehensive bundle of 9 ebooks.

What's Included:

  • Getting Started with R
  • R Programming for Data Science
  • Data Visualization with R
  • Financial Time Series Analysis with R
  • Quantitative Trading Strategies with R
  • Derivatives with R
  • Credit Risk Modelling With R
  • Python for Data Science
  • Machine Learning in Finance using Python

Each book comes with PDFs, detailed explanations, step-by-step instructions, data files, and complete downloadable R code for all examples.