Games of Chance: Probability Lab

You need: Two dice per pair · Tally sheet · Pencil

1. Player A wins if the difference between the two dice is 0, 1 or 2. Player B wins on 3, 4 or 5.
2. Predict who will win more often.
3. Play 30 rounds and tally the winner of each.
4. Draw a 6 × 6 table showing every possible difference.
5. Count the ways each player can win and compare with your tally.

How you'll know: You can show with the table that A has 24 of the 36 outcomes, and explain why your 30 rounds might not show exactly that.

Go further: Change the rules so that the game becomes fair. Prove it with the table.

You need: A coin each · Tally sheet · Class spreadsheet or wall chart

1. Flip your coin 30 times and record heads and tails.
2. Work out your percentage of heads.
3. Add your results to the class total, one pair at a time.
4. After each pair is added, work out the class percentage of heads and plot it on a line graph.
5. Describe what happens to the line as the number of flips grows.

How you'll know: Your graph shows the percentage of heads swinging a lot at first and then settling close to 50%.

Go further: Find out about John Kerrich, who flipped a coin 10,000 times. How close did he get to half?

You need: Two dice · A race track drawn with 11 lanes numbered 2 to 12 · Counters

1. Put a counter at the start of each lane.
2. Roll two dice, add them, and move that lane's counter forward one step.
3. Keep going until one counter reaches the finish (8 steps).
4. Run three races and record the winners.
5. Use a 6 × 6 table to find how many ways each total can be made.

How you'll know: You can explain why 7 has a 6/36 chance, while 2 and 12 have only 1/36 each.

Go further: Change the race to use the product of the two dice instead. Which lane is favourite now?

You need: Card · Protractor · Compass or round lid · Split pin or pencil and paper clip · Coloured pencils

1. Choose probabilities that add to 1, for example 1/2, 1/4, 1/6 and 1/12.
2. Work out each sector angle: 360° × probability.
3. Draw the circle, measure the angles and colour the sectors.
4. Spin 30 times and record each colour.
5. Compare the experimental results with the theory, then pool with another group.

How you'll know: Your sector angles add to 360° and your pooled results move closer to the probabilities you chose.

Safety: Take care with compass points and split pins.

Go further: Design a spinner that looks fair but isn't. Can another group spot the trick?

You need: Paper or plastic cups · Tally sheet · Bottle caps (optional)

1. Drop a cup from the same height 30 times and record how it lands.
2. Work out the experimental probability of each landing.
3. Combine with other groups to get 100 or more drops.
4. Compare the 30-drop and 100-drop probabilities.
5. Discuss why you can't work this out with a sample space like a die.

How you'll know: You can give a probability estimate for each landing and explain why more trials make it more reliable.

Safety: Use cups or bottle caps rather than drawing pins. Drop from a safe height, not standing on chairs.

Go further: Test a bottle cap too. Knucklebones, one of the oldest games of chance, worked the same way.

You need: Opaque bag · 10 counters in two or three colours · Tally sheet

1. A partner secretly puts 10 counters in a bag.
2. Draw one, record the colour, and put it back. Shake the bag.
3. After 20 draws, predict how many of each colour are inside.
4. Do 30 more draws. Update your prediction.
5. Open the bag and compare.

How you'll know: Your prediction after 50 draws is closer than after 20, and you can explain why.

Go further: What is the probability of NOT drawing red? Use the complement of your estimate.

You need: Your game equipment · Recording sheet · Calculator or spreadsheet

1. Write the rules and the theoretical chance of winning.
2. Play the game 100 times, recording win or lose each time.
3. Every 10 plays, work out the percentage of wins so far.
4. Plot the running percentage on a line graph with the theoretical probability as a line across it.
5. Decide whether the game behaves as you predicted, and change it if not.

How you'll know: Your graph shows your results settling near the theoretical line, and your poster matches the evidence.

Safety: If you use food as prizes, check for allergies first.

Go further: Work out the expected number of prizes the stall will give away for 200 players.