IPS - Day 25

Today we finished the 39-Game Hitting Streak investigation.No issues came up in this discussion. Students understood what they did to calculate the probabilities and simulate the situation.

We then looked at the game show Deal or No Deal to investigate expected value and its use. The first task, which everyone readily got, was to determine the probability of picking the $1 million case. The next task turned out to be more difficult.

Students were asked to calculate the expected value of the brief case that was selected. There was a lot of discussion and confusion. I told the class they needed to create a probability model for the game. Again, this was a struggle. Finally, with some coaching and a simplified example, students began to create their probability model and calculate the expected value, which cam out to $131,477.54.

There was a discussion about what this value represented. I used the analogy of starting with the show's first airing and summing the values of every case that has been selected on the show and then calculating the average. The average value over all of the shows should be close to the $131,477.54. Another way of thinking of the value is to consider that if you were able to repeatedly play the game thousands upon thousands of times, the average value of the cases you pick would be close to the $131,477.54 value.

We then played the game. I like to keep track of the expected value at the end of each round and discuss this value versus the expected value. This allows students to think about the expected value versus the probability of actually having a winning case. At one point in the game there were 5 cases left. Three cases were valued at $50,000 or less, one had a value of $100,000 and one a value of $500,000. The deal was to take a guaranteed $53,000.

I explained that the probability of having a case less than this value was 3/5. The question of having a much larger expected value ($130,000) versus the chance of cashing in on the higher value comes into play. On the next turn the offer was $67,500 and there was only one case with a value higher than this. Again the probability of actually holding the case was only 1/4 while the expected value was $137,536. Again, in a situation like this, since you aren't able to play the game repeatedly, it would make more sense to accept the offered amount.

This is always a fun activity that students get into, especially as you go around the room and have different students select which case to open next. It also provides a nice example of relying too much upon making use of expected value exclusively when making decisions.

Next class will focus on practicing creating and using probability models.

View the class summary for a student's perspective and to view the lesson slide.