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Purpose of Project * To carry out simple experiments to determine the probability that the sum of two dice when thrown is equal to seven.

Variables * Independent- sum * Dependent- number of throws * Controlled- Cloth covered table top.

Method of data collection 1. Two ordinary six-faced gaming dice was thrown 100 times using three different method which can be shown below. i. The dice was held in the palm of the hand and shaken around a few times before it was thrown onto a cloth covered table top. ii. The dice was placed into a Styrofoam cup and shaken around few times before it was thrown on a cloth covered table top. iii. The dice was placed into a glass and shaken around a few times before it was thrown onto a cloth covered table top. 2. All result was recoded and tabulated. 3. A probability tree was drawn.

Presentation of Data

Throw by hand Sum of two dice | Frequency | 23456789101112 | 4485161516121172 |

Throw by Styrofoam cup Sum of two dice | Frequency | 23456789101112 | 2513112081481072 |

Throw by Glass Sum of two dice | Frequency | 23456789101112 | 18910121214121174 |

Sum oftwo dice | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | Total | Experiment1 | 4 | 4 | 8 | 5 | 16 | 15 | 16 | 12 | 11 | 7 | 2 | 100 | Experiment2 | 2 | 5 | 13 | 11 | 20 | 8 | 14 | 8 | 10 | 7 | 2 | 100 | Experiment3 | 1 | 8 | 9 | 10 | 12 | 12 | 13 | 12 | 11 | 7 | 5 | 100 | Total | 7 | 17 | 30 | 26 | 48 | 35 | 43 | 32 | 32 | 21 | 9 | 300 |

Table showing result from the three experiments

Analysis of Data

Probability tree showing the theoretical way of obtaining the probability of two dice

We can use the table to see that there are six ways to get a sum of seven with two dice: (1,6),(2,5),(3,4),(4,3),(5,2),and (6,1).There are a total of 36 outcomes. Probability=Possible outcome Total outcome =6 36 =1 6 From this experiment the table shows that there are 35 way in which the sum of seven was obtained with two dice. There are a total of 300 outcomes. Probability=Possible outcome Total outcome =35 300 =7 60 This experiment compare the theoretical probability from the observed probability for 100 throws under each of three different conditions. These condition have significant influences in the outcomes of these throws.1 the size of the cup chosen may have a particular influence on these outcomes.2 the inside surface of the two types of cups chosen are also factors that may influence these outcomes. These simple experiment were intended to give some idea of the theory of theoretical probability. The range between the theoretical probability and the probability obtained from the experiments is major. This is so since the theoretical probability is 1/6 and the observed probability is 7/60. They must have been some effects that influences this major range, some of which can be the surface of the table and the way the dice was thrown. The range = largest observation-smallest observation = 1/6 – 7/60 = 3/60

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