Which game to win?

  Investigating strategies to measure probability.......

                     

You are on a TV game show.  

To win 1 million francs, you have a choice of playing one of these games.

Which would you choose to play & why?

Game A	Game B
Flip 2 coins and if they both land         on heads, you win.	Pull a royal card out of a pack of cards     and you win. (Shuffled pack without         jokers )
Game C	Game D
There are 2 balls hidden beneath a      set of 6 cups. Choose 1 cup; if the      ball is beneath it, you win.	Roll two dice; if you roll a double, you     win.

In pairs, students investigated the probabilities of winning each game to determine which would have the best odds of playing to win 1 million francs.

To help visualise and better understand the probability games, they were given a pack of cards, 2 dice, 2 coins and access to some cups.

(Students in pairs working out how to measure the probability of each game)




After measuring the possible probabilities, we shared our conclusions and the different strategies we used.   The coin flip became quite an interesting discussion with lots of us sitting on the fence on how to measure it. Students had posed two possible ways of measuring:
      

Eventually, one student explained that we need to view each coin as an independent variable like we do with science experiments (Wow!) and so that is why we should measure the probability as being a 1 in 4 chance.


Looking at our measurements we then ordered each game from the highest to lowest probability of winning.  This became another great discussion with lots of different opinions. At first, the majority of us felt that the order of probability was game C, A, D and then B.  Eventually, we realised we need to measure each using decimals or percentages because the fraction form was too tricky to understand.  After converting the probabilities to percentages, we could more easily see the correct order.   And so, therefore , the best game choice to possibly win the money was Game C. 

                    

Reflection:

We looked at our central idea again: 

We discussed how this activity might have helped us understand our central idea more or whether our thinking had changed.   We also discussed if we can see now how measuring probability is mathematical thinking.