This isn’t an approach I’ve seen much before, and so it may not be wise to do this your first time (I also recommend adapting this explanation), but maybe focus on that Bayes’ theorem is when you have two competing hypotheses, and you get evidence that is more probable under one hypothesis than the other.
When you get evidence, you keep track of the probability of each hypothesis separately, but what matters is their normalized probability. (I’ll use frequencies since those are easier for people to manipulate than probabilities.) You might start off with the knowledge that the chance someone has a rare disease is 100 out of a million, but the chance that someone has a common disease is 9,800 out of a million. Everyone with the rare disease goes to the doctor, but only half of the people with the common disease go to the doctor, and no healthy people visit the doctor- so in a city of one million people, 100 people with the rare disease visit the doctor, and 4,900 people with the common disease visit the doctor, and the probability someone at the doctor’s office has the rare disease is 2%.
Then the doctor runs a test- it gives an A result 99 times out of a hundred for people with the rare disease, and a B result 1 time out of a hundred for people with the rare disease. It gives an A result 2 times out of a hundred for people with the common disease, and a B result 98 times out of a hundred. Now we have 99 people with rare and A, 1 person with rare and B, 98 people with common and A, and 4802 people with common and B. Of the people who got an A result, they have about a 50% chance to have either disease- but of people with a B result, almost all of them have the common disease.
The main mental strategy that Bayes’ theorem helps people with is “keep multiple hypotheses in your head at once,” and you may want to emphasize that to people just hearing about it.
This isn’t an approach I’ve seen much before, and so it may not be wise to do this your first time (I also recommend adapting this explanation), but maybe focus on that Bayes’ theorem is when you have two competing hypotheses, and you get evidence that is more probable under one hypothesis than the other.
When you get evidence, you keep track of the probability of each hypothesis separately, but what matters is their normalized probability. (I’ll use frequencies since those are easier for people to manipulate than probabilities.) You might start off with the knowledge that the chance someone has a rare disease is 100 out of a million, but the chance that someone has a common disease is 9,800 out of a million. Everyone with the rare disease goes to the doctor, but only half of the people with the common disease go to the doctor, and no healthy people visit the doctor- so in a city of one million people, 100 people with the rare disease visit the doctor, and 4,900 people with the common disease visit the doctor, and the probability someone at the doctor’s office has the rare disease is 2%.
Then the doctor runs a test- it gives an A result 99 times out of a hundred for people with the rare disease, and a B result 1 time out of a hundred for people with the rare disease. It gives an A result 2 times out of a hundred for people with the common disease, and a B result 98 times out of a hundred. Now we have 99 people with rare and A, 1 person with rare and B, 98 people with common and A, and 4802 people with common and B. Of the people who got an A result, they have about a 50% chance to have either disease- but of people with a B result, almost all of them have the common disease.
The main mental strategy that Bayes’ theorem helps people with is “keep multiple hypotheses in your head at once,” and you may want to emphasize that to people just hearing about it.