**We imagined the following:**

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

Flip 2 coins.

If they both land on heads, you win.

If they both land on heads, you win.

Game B

If you pull a royal card out of a pack cards, you win.

Game C

There are 2 balls hidden under a set of 6 cups.

Choose 1 cup.

If a ball is beneath it, you win.

Choose 1 cup.

If a ball is beneath it, you win.

Game D

Roll 2 dice.

If you roll a double, you win.

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.

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.

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:

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:

Someone 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.

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:

- How did this activity help us understand our central idea?

- How has our thinking changed about probability?

- Why is probability mathematics?

- How did this activity help us understand our central idea?

- How has our thinking changed about probability?

- Why is probability mathematics?

With everyone understanding how we can measure probability and that is why it is mathematical thinking as well as the clear connection we can make with fractions / decimals / %, our understanding had certainly deepened a lot.