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Part A - Cat and Mouse Game - Knowledge and Procedures
Q1- My first impression from looking at the board game is that I will lose. This is because the room that holds the mouse is closer to the cat than the room that has the cheese.
Q- a) First 10 trials (O = Odd, E = Even)
1- OOE - W 6- OO - L
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- OO - L 7- EEOE - W
- OO - L 8- OEOE - W
4- OO - L - OO - L
5- EOO - L 10- EOE - W
Total - 4 wins (W) and 6 loses (L)
The results from these 10 trials does not change my initial prediction because the chance of losing is higher than winning.
b) Next 40 trials (O = Odd, E = Even)
11- OEE - W 1- EOO - L 1- OEOE - W 41- EOE - W
1- OEE - W - EOE - W - OEE - W 4- EOO - L
1- OEE - W - OO - L - OO - L 4- EOO - L
14- EEE - W 4- OO - L 4- OO - L 44- EEE - W
15- OEE - W 5- OO - L 5- EOO - L 45- OO - L
16- EOE - W 6- OO - L 6- OEE - W 46- EOE - W
17- EOO - L 7- EEE - W 7- EEE - W 47- EEE - W
18- EOO - L 8- EOO - L 8- EEE - W 48- EOO - L
1- OEE - W - OEE - W - OEE - W 4- EEE - W
0- OEOO - L 0- EOO - L 40- EEOO - L 50- OEOO - L
Total - 1 wins (W) and 1 loses (L)
The results from these trials does change my initial prediction in the fact that there is a higher chance of winning. These results also contradict the results from Q a)
Modelling and Problem Solving
Q -
Tree Diagram -
All Possible Outcomes -
1. OO - ½ x ½ = 1/4 L
. OEOO - ½ x ½ x ½ x ½ = 1/16 L
. OEOE - ½ x ½ x ½ x ½ = 1/16 W
4. OEE - ½ x ½ x ½ = 1/8 W Chances
Winning = 56%
5. EOO - ½ x ½ x ½ = 1/8 L Losing = 44%
6. EOE - ½ x ½ x ½ = 1/8 W
7. EEOO - ½ x ½ x ½ x ½ = 1/16 L
8. EEOE - ½ x ½ x ½ x ½ = 1/16 W
. EEE - ½ x ½ x ½ = 1/8 W
Discussion -
From the analysis of the outcomes, it shows that this board game actually advantages the mouse. Unlike my initial prediction that it would advantage the cat. From looking at the above calculations, there is a 56% chance of throwing a winning game (this means that you can throw any one of the 5 combinations that lead you to the cheese) whereas there is only a 44% chance of throwing a losing game ( throwing any one of the 4 combinations that lead you to the cat) 5 out of the combinations results in a winning game, where only 4 of the combinations results in a losing game.
With each throw there is a 50% chance of either throwing a odd or an even number, this never changes. It would not matter how many times you threw the dice, there would always be an even chance of throwing even or odd numbers.
Part B - 'Practice makes Perfect'
Knowledge and Procedures
Q1 - Before
Success Failure
p = Success 1/1
q = Failure 1/1
Q - Practice Sheet
Date and Time 10/07
10pm-10.0pm 11/07
10.0pm-10.45pm 1/07
10.10pm-10.5pm 1/07
11pm- 11.10pm 14/07
10.0pm- 10.40pm
Day 1 4 5
Win 1 17 1 4
Lose 1 14 10 8 7
Q - After
Success Failure
p = Success 4/1
q = Failure 7/1
Q4- Binomial Probability Distribution Tables
Before -
x 1 4 5 6 7 8 10
p(x) 0.047 0.14 0.6 0.4 0.18 0.0 0.05 0.008 0.001 0.000
Total = 0.88
After -
x 1 4 5 6 7 8 10
p(x) 0.000 0.000 0.001 0.010 0.041 0.117 0.0 0.6 0.5 0.077
Total = 0.7
The above tables have been calculated by using the rule
Q5 - Histograms
Before -
After -
Q6 - The skill being learnt here is tossing a paper ball into a waste paper basket. The paper ball was 6cm in diameter and was thrown over arm from metres away, into a waste paper basket that was 7cm high and 5cm in diameter. The effect of doing this trial for over a week was to investigate if the comment 'Practice makes Perfect' is correct. After analysing the data that has been collected, the comment has been proven to be correct. By looking at the Binomial Probability Distribution tables and graphs this can be shown. When looking at the table, the total added up in the before table is 0.88 whereas in the after table it is 0.7. This proves that it has become closer to 1. When looking at the graphs, it is shown that in the before histogram, the graph is towards the first half (lower numbers) and then goes down to a 0.000 at the end whereas in the after graph, the graph is more towards the last half and is higher at this end (higher numbers). All this proves that with practice it becomes more likely that you will achieve a success rather than a failure.
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