The Probability Stacking Fallacy
In the world of 'wouldn't it be nice if' it is assumed that all things are possible, it's just that some things are very improbable. Douglas Adams ridiculed this idea with the concept of the Infinite Improbability Drive, where it was merely necessary to compute the exact probability of jumping spontaneously to the desired spot in the universe in order to have it happen. The object of this essay is to challenge the assumption that one can merely add the probabilities of a sequence of events together and thus come up with a valid probability for the whole sequence occurring. The example I would like to use is that of a driver who always drives the same route to work, and calculates the possibility of being stopped at each of the ten sets of traffic lights that they must traverse. They want to discover the likelihood of getting to work without being stopped at any traffic light if they attempt the journey so early that there is no other traffic. They accept that they ma...