# Probability Simulations

I’m teaching a probability unit currently with a low ability Year 8 group.  I really enjoy teaching probability and try and teach this sort of age and ability group it through games.  I’d been looking for some alternatives to the old “racecourse derby” type of game with two dice.

I came across ideas around the following three areas which I’ve tweaked myself.

Game 1 – Probability bingo

Pupils get to choose 8 numbers from 2 to 12 to put on their bingo card.  They can use a number more than once if they wish.  At this point we have not discussed the probabilities of different sums coming up so they are doing this ‘blind’.  We play the game a couple of times (they tweak their bingo cards the second time based on their observations the first time).  I used activ and the random dice on that but you could do it with 2 normal dice.

After a couple of games we discuss the results and we look at sample spaces as a way of showing every possible outcome and how often each outcome can be generated.  They then design their bingo card with the optimal numbers for them to win.

It is useful, through all the games, to keep a running total of the scores as you can then compare theoretical probability to real life data.

Game 2 – Who Will Win

This is particularly useful if you are teaching in an area where football support tends to be bi-polar (Sheffield is perfect and with be being a Sheffield United fan, even more so).

The idea is to simulate a 2-goal game of football – the game ends when 2 goals are scored.  The instructions are on the powerpoint – I make a big play of being fair as I’ve given each team 3 possible outcomes (we use the difference between the scores on 2 6-sided dice).  Being a Sheffield United fan of course I’ve loaded the game in my teams favour, but they don’t realise this yet and I don’t tell them.

We then play a couple of games to show them how it works and then they ‘simulate’ a 36 game season (you can change the number of games).  They then collect data and decide whether the game was fair or not – and of course they can re-design the game to make it fair if they wish.

Game 3 – Release the Prisoner

I saw this on an American site and really liked it and tweaked it a little.  Students start with 6 counters and they can place their counters in any of the cells.  Each counter represents one prisoner than needs to be released.  Two dice are thrown and you can decide whether to go with the sum or the difference (I have sheets for the sum and difference of 2 6-sided dice and the difference with 2 10-sided dice).  If the sum/difference matches a cell with a counter on it, they can release one of their prisoners.  If they have more than one prisoner in that particular cell, they can only release one of them.  The winner is the first person to release all 6 prisoners.  This game could be played in pairs if you wish or you could be the dice thrower.  Again you can discuss, maybe with the use of sample spaces or similar, the optimal cells to place your prisoners in to give you the best chance to win the game.

All the games are on the powerpoint and I’ve given word and PDF files for the bingo cards, the Who Will Win worksheet and the different grids for Release the Prisoner.

Let me know if you find these resources useful.

The powerpoint:

Probability Games

Bingo Grid

Two Dice Bingo Grid (Word)

Two Dice Bingo Grid (PDF)

Who Will Win worksheet