Tackle Likelihood to Avoid Risk and Make Choices, while Using all You Know and Avoiding Decision-destroying Fallacies
Use the science of probability to turn vague terms like “likely” into precise values you can use to assess risks and alternatives. This beginning course gives you all you need to apply probability to real-world questions. Use Bayes’ Rule to incorporate your contextual knowledge. Combine simple probabilities to assess complex events. Use conditional probability to focus on groups or situations. Draw correct conclusions from conditional probabilities, including false positives and false negatives. Avoid the many probability fallacies that often lead to bad decisions. Try out your knowledge in exercises, then take on some tricky challenges (you’ll get the solutions). A formula “cheat sheet” and optional spreadsheets are included.
What You’ll Learn
Probability is both a science and a measure of likelihood. We go beyond the standard examples of cards and dice and discuss what it means for weather prediction or medical tests. Probability is useful for giving you an expected value, what you would expect the outcome to be on average. At the same time, it helps you think about the unexpected.
By the end of this course, you will be able to:
- Avoid the probability fallacies that often mislead people. Probability appears simple and straightforward, which leads people to get misled by various common probability fallacies. One key fallacy is seeing patterns that aren’t there. You will see examples in which ordinary randomness leads to silly conclusions. Another is the confusion of the inverse of conditional probabilities. This causes confusion in assessing the results of medical tests and making ridiculous causal connections.
- Calculate probabilities using cases and historical data. Many probability calculations are built on simple equally-likely events. Historical data, such as sales, can be used to predict the likelihood of events of interest happening, even focusing on particular groups or situations. For example, a bank uses its data to find the job category most likely to go into default on their loan.
- Calculate the probabilities of complex events based on simpler ones. Often the event you’re interested in is built up from other events. Examples are all roles must be filled or at least one machine must be operational. You will have some exercises to apply these techniques and some challenges (with solutions) that have baffled great minds.
- Apply Bayes’ Rule to bring outside knowledge into your probability estimates. Bayes’ Rule uses knowledge about the context and the environment to modify collected statistics for a more realistic probability estimate. It also avoids the confusion of the inverse and makes sense of false negatives and false positives.
- Use expected value to assess and compare alternatives. You’re interested in probabilities primarily as a tool to get expected values, such as the amount of money you expect to make on a line of products in an uncertain market. You will calculate expected value by breaking the problem into cases. You will apply these techniques to compare strategies in the game of Wordle.
- Focus your analysis on segments or situations using conditional probability. You often want to take action to decrease risk probabilities or increase probabilities of desired outcomes. The new probability is conditional on the action. Conditional probabilities are also used to focus in on groups, such as finding the customers most likely to buy the product.
- Reason correctly using false positives and false negatives. You’ll see that a prediction that’s “right 90% of the time” may not be useful. Even doctors often assume a test will perform much better than it actually does.
- Develop intuition about randomness. We use a random number generator to show examples of randomness at work. Optionally, you can run it yourself using a spreadsheet. Part of learning probability, especially if you’re doing risk analysis, is to expect the unexpected.