We are working through Mosteller’s 50 Challenging Problems in Probability this fall. Today we tackled problem #3 which is an problem that is definitely accessible to kids and has a fun and surprising result.

The problem can be summarized like this:

You have two people who each have probability p of making a correct decision and a third person who just flips a coin. If this group of three reaches a decision by majority rule, what is the probability that they make the correct decision?

I started the project today by sharing this problem with the boys and asking them what they thought:

They had a pretty good idea about how to approach the problem, so for the 2nd part of the project we dove in to the calculation and found the surprising result:

To wrap up, we wrote a short computer program to simulate the problem and see if the results of that program matched what we’d found in the second part:

I really like this problem – easy for kids to understand, not too difficult to compute the answer, the computation allows a few different approaches and lessons about probability, and the result has a nice surprise! Fun project ðŸ™‚