The story of Martin and Big Fish, taken from ‘An Introduction to Probability and Inductive Logic’ by Hacking, is about risk and insurance.
Marting sells clothes on the streets. His sales are typically about $300 and cost $100. Since he is not registered as a vendor at that location, he gets tickets from the authorities for illegal sales. The fine is $100, and he estimates that they happen about two times on his 5-day week.
The daily expected value of his work is:
(2/5) x (300 – 100 -100) + (3/5) x (300 – 100) = $160.
Now, Big Fish finds Martin offers his stall at a daily rent of $50. Martin’s new return can become 300 – 100 – 50 = 150. Should he agree with this?
It is a trade-off for Martin; his profits come down, but he runs no risk now. It is possible that the number of raids increase in future. The same can happen with the fine amount. By paying the additional $10, he replaced the risk with certainty.
Reference
An Introduction to Probability and Interactive Logic by Ian Hacking
