**i. How to Play the Game**

ii. Demonstration of Apparatus

iii. Probability Calculations

iv. Differences Between Pairs

v. Statistical Analysis

ii. Demonstration of Apparatus

iii. Probability Calculations

iv. Differences Between Pairs

v. Statistical Analysis

How to Play the Game

**A Day at the**

Data Carnival

Data Carnival

We will now show you a demonstration of our game being played!

Magnet Game - Cut lawn decoration to create the fishing rod. Tape and string were used to make the fishing line, with a magnet attached to the end. A bucket was used; placed 12 magnets in the bucket to randomly draw from.

Dice - Made from paper. Folded into a 6-sided cube and pictures were hand drawn onto each side.

Spinner - Made using a turntable and record. Sectioned off into 6 sides to distinguish each category.

**Demonstration of Apparatus**

Stage 1

**Probability Calculations**

First, grab a Data Carnival Scorecard from the Carnival Chest.

Ask yourself, how many times (cumulatively) have you visited a carnival or circus?

0-2 times: 100 points (A and B)

3-4 times: 500 points (A and B)

5+ times: 1000 points (A and B)

Spin the 6-section spinner 3 times - take note of your results. (2 sections are clowns, 2 sections are magicians, and 2 sections are ferocious lions).

Land on lion 2 times: 1000 points (A) or -1000 points (B)

Otherwise: 0 points (A) or 1000 points (B)

Differences Between Variant A & B

Stage 1:

Stage 2

Stage 3

The probability calculations for Stage 1 were simple; three possible point groups which means that a player has a l in 3 chance of being in any of the categories.

Stage 2:

Pick up the pair of standard 6-sided dice and prepare to roll them up to 5 times.

Roll the dice 3 times. If you haven’t received a composite sum greater than 6 after 3 rolls, you still have a chance. Roll another two times. If you do not roll a composite sum greater than 6 for the first time within 5 rolls, stop rolling the dice!

Within 3 rolls: 500 points (A) or 1000 points (B)

On 4th or 5th roll: 200 points (A) or 300 points (B)

Otherwise: 0 points (A) or -700 points (B)

Statistical Analysis

Our resultant winning percentage was within 1 percent of our probability of winning (B)

The spinner is a binomial calculation as each repeated trial is independent and without bearing on the outcome of the next; the outcome was either a success or failure. We calculated the probability of landing on 2 lions with 3 spins. We also calculated the probability of not landing on two lions (prime). The probability of getting 2 lions is 0.2222 and otherwise is approximately 0.7778. The chances of landing on 2 lions in 3 spins is much harder than getting otherwise.

Stage 4:

Stage 3:

How to Play the Game Cont.

Use the rod to draw 2 magnets (one after the other) from an assortment containing 12 colour-coded magnets (4 red magnets, 4 blue magnets, 3 yellow magnets and 1 white magnet).

Careful! if you pick up more than one magnet, take the top one and return the others to the assortment.

Pick 1 red and 1 blue: 1000 points (A) or 800 points (B)

Pick 1 white: -400 points (A) or -1000 points (B)

Otherwise: 0 points (A) or 100 points (B)

Criteria for Winning:

We hope you enjoyed your stay at the Data Carnival!

You WIN the game if you’ve accumulated 1300 points or more (A) or 1600 points or more (B). If not, there’s no need to worry - remember that you’re always welcome to play again!

Stage 4:

The final stage is the fishing game which is an example of hypergeometric probability. This is because there's a specified number of dependent trials in which the magnets are drawn without replacement.

We had 4 red, 4 blue, 3 yellow, and 1 white magnets for a total of 12 magnets. The probability of getting 1 red and 1 blue is 0.2424. The probability of 1 white magnet is 0.1667 and otherwise is 0.5909.

The calculation for the white magnet is different than the other magnets because it only takes one white magnet to receive the corresponding points.

Stage 3 involved rolling the 6 sided dice five times. This is a geometric calculation since it has a specified number of independent trials with two possible outcomes (success or failure); there was also a waiting time involved.

The probability of within 3 rolls was high with a probability of 0.739098. The probability of within 5 rolls was significantly less at 0.1544 and otherwise was 0.106502.

There were no significant differences in Stage 1.

Stage 1

Stage four- Fishing: Variant A- (Pick 1 red and 1 blue - 1000 Points)

(Pick 1 white - -400 Points)

(Otherwise - 100 Points)

Variant B- (Pick 1 red and 1 blue - 800 Points)

(Pick 1 white - -1000 Points)

(Otherwise - 100 Points)

Stage 1

Stage 2

Stage 3

Stage 4:

General apparatus included the Carnival Chest, score cards, and instruction sheets.

Mode = 1500 (A)

Mode = 2600 (B)

Both Modes were winning scores.

Both games had a mean that would be a losing score.

Mean = 1229.0323 (B)

Mean = 1277.4194 (A)

Line of Best Fit:

Correlation Coefficient is 0.3953 (A). Correlation Coefficient is 0.5671 (B). Both yielded a moderate positive correlation between visits to the carnival and points won

18 people out of 31 who played won our game (A and B)

y=81.1x+1020 (A)

y=292.73x+312.79 (B)

**Andy F. | Zak H. | Mitchell M. | Zak O.**

Probability Calculations

Cont.

Stage 2

Stage 3

Probability Calculations

Cont.

Thank you for listening to our presentation.

We hope you return to enjoy the never-ending fun of the Data Carnival!

Whether or not a person landed on two lions was a deciding factor in winning or losing in either of the two variants.

Land on lion 2 times: 1000 points (A) or -1000 points (B)

Otherwise: 0 points (A) or 1000 points (B)

The difference of winning 1000 points or losing 1000 makes a notable difference in who wins or loses the game.

**THE END**

Players earned more points in Variant B for rolling a composite sum greater than six, though a penalty also existed if this sum was not rolled.

Differences Between Variant A & B

Stage 4

Within 3 rolls: 500 points (A) or 1000 points (B)

On 4th or 5th roll: 200 points (A) or 300 points (B)

Otherwise: 0 points (A) or -700 points (B)

Pick 1 red and 1 blue: 1000 points (A) or 800 points (B)

Pick 1 white: -400 points (A) or -1000 points (B)

Otherwise: 0 points (A) or 100 points (B)

Several small differences exist in Stage 4, most notably in terms of the points lost for withdrawing a white magnet.