This is far too much for a 50 minute lecture, you would be lucky to be able to effectively cover this material in five hours.
When lecturing you want to repeat every important point several times and leave lots of time for discussion.
You could discuss what probability means, ask some simple questions such as the odds of getting a one or two when rolling a six sided die, and then you could have them work together to guess at some real life probabilities. You could, for example, give them the probability of dying each year in a car accident if you do wear a seatbelt and then ask them to estimate the probability of death for drivers who don't wear seatbelts.
This is far too much for a 50 minute lecture, you would be lucky to be able to effectively cover this material in five hours.
Agreed. You could easily spend 50 minutes just on Bayes' Theorem (look at the length of Eliezier's intuitive explanation) or just on Monty Hall (it's a famous puzzle because people are easily confused about it). Don't underestimate the inferential distance or the time it takes to close it.
Here are two options that could work:
Option A: focus on estimating likelihood in everyday life. Have lots of examples, and talk about how they came up with their answers so that you can explore different methods of estimating likelihood. In some cases estimating likelihood is more like a calculation (e.g. in Fermi problems), in some it uses a heuristic like availability or representativeness, and so on. You can include some examples where a heuristic leads to a wrong answer so that you can talk about biases, but I'd first include an example where the same heuristic is useful. No Bayes theorem.
Option B: Focus on Bayesian updating as the logic behind everyday plausible reasoning and science. Give a very intuitive, brief explanation of Bayes' Theorem as the rules for updating beliefs based on evidence. (Use few or no equations. They should be able to see that there are rules for updating and have a rough intuitive sense of how it works, but you shouldn't expect them to be able to do Bayesian calculations.) Go through a few examples, including some from everyday life. Then talk about the scientific process, and the Bayesian logic that underlies it. Use examples. Nothing on heuristics & biases research.
Maybe you could give them the url to Eliezer's intuitive explanation as something to read if they want to learn more (if you think they're the kind of students who might actually check it out).
I agree that your agenda seems over ambitious. If you want to do probability, I would suggest warming up with the Buffon needle problem and then using Bertrand's paradox as the main course. Monty Hall and St.Petersburg paradoxes are also good.
Buffon's Needle will likely require more math than many highschool students even bright highschool students have. If they don't have integration, Buffon's Needle is tough.
Hmmm. Maybe math is done more rigorously and less intuitively these days. When I was in high school, Buffon was done in three simple steps.
Change the length of needle and change the problem from probability of line-crossing to expected count of line-crossings.
What happens to the expected count if the needle is bent?
What happens if you bend a needle of length pi into a circle and drop it on a ruled sheet with spacing of 1 unit?
Yes, this is the beautiful conceptual solution to the problem, but it's not universally known. I saw it in these two places:
Yes, that seems quite nice. I had not seen that approach before (or if I have have no recall of it).
Common mistakes about probability. I'm generalizing from one example plus some exterior evidence, but hearing about people getting things wrong tends to get my attention.
One key elementary concept is the distinction between probability and statistics. Failing to make this distinction can lead to a lot of confusion. Consider the following two problems:
The two questions have a superficial similarity, but are in fact totally different. The first question has an unique correct answer. The second question does not; it is not even clear what it would mean to say one answer is "correct" and another "incorrect". This is where all the philosophical problems begin.
One possibility that might catch their interest is the use of particle fliters in robotics.
It is topical, with Google's announcement of robot cars which I think uses ideas based off them.
I'm going to have the opportunity next month to lead a 50-minute lecture/discussion about a subject of my choice. The audience will be about 20 high-school students, and they'll be there because they want to hear about whatever subject I choose. I can't make any assumptions about their background, except that they'll be interested.
This is a completely wild guess, but are you doing MIT Splash?