The Game Show Problem

This is a problem which I have found stimulated my ideas about analysing probability.

The interesting part is justifying the decision.

Pretend you are on a gameshow. The gameshow host shows you three identical doors and tells you: "Behind one of these doors is a brand new car. If you pick the right door, the car is yours!" You think about it...and choose one of the doors. The host asks you, "Do you want to lock that in?" You reply, "Yes. Lock it in."

Then the host opens one of the two remaining doors that you did not choose. It is empty. "Phew," you thought, "I'm glad I didn't choose that one". Then comes the interesting part. The host asks you, "Do you want to change doors?"

What would you do? Why?

Probability Clothes Line

The Resource:

This resource consists of a piece of string, tiny wooden pegs and a number of small shirt-flashcards, each containing a "probability word".



How to use this resource:

Divide the flashcards evenly among the children participating in this activity.

Ask the children to come hang their shirts out on the line in order, from the probability word which signifies "least like to occur" to most likely.

Go through each of the words and discuss the reasoning that justifies their choices.

Also ask the students to suggest events that have the corresponding probability of occurring in relation to each of the words. E.g. likely - that it will rain tomorrow.

Alternative to using the pre-written shirts, ask children to write their own probability words on blank shirts instead.

Mathematical focus/outcome:

Strand: Chance and Data

Outcomes QSA (2004):
1.1 Students use everyday language when commenting on aspects of chance in practical activities and familiar events.

2.1 Students identify and classify familiar events according to the likelihood of occurrence.