When Blaise Pascal and Pierre de Fermat studied a problem related to a gambling game they developed what is now widely known as the probability theory.
They were hired by two very rich man, that were interrupted in a middle of a gambling game, to determine in which proportion the stakes should be divided based on the current score.
The formula of total probability is widely used and is very significant in the probability theory.
The fun fact is that the interest in probability was solely influenced by gambling games throughout the 17. 18. and 19. century. Only way later was probability studied for theoretical reasons. 
Related articles
- Guide to Game Theory: expected value and independent events (thefinalwager.co)
- Struggling with chance (plus.maths.org)
- Pierre de Fermat and His Mathematical Legacy (math.answers.com)
- What is a Probability? (math.answers.com)
- Total Probability Theorem and Bayes Theorem (jyyuan.wordpress.com)
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