Purpose of Project / Aim:
Probability is an educated thought or guess to determine if a particular event will occur. Probability is important to assist in making and predicting everyday decisions; the probability that a child will be born with sickle cell disease or the probability that crops will die are all important for the human survival. The use of M&M’s is to substitute for the examples listed above to examine probability considering they are used in everyday life and are therefore readily accessible. When individuals consume M&M’s, they indentify particular colours and this can be related to probability. Calculating the probability of a particular colour is mainly based on the total number of M&M’s you have and how much of that colour is present. This is because the general formula for probability is interest over the total: P(A) = The Number Of Ways Event A Can Occur
The total number Of Possible Outcomes
Standard deviation is the value calculated to indicate the extent of deviation for a group as a whole. Standard deviation will be used to assist with the analysis of this experiment. This experiment aims to determine whether the portions of each colour in each bag of M&M’s are even by determining the probability of picking a particular colour and if not by how far “off” they are.
Method of Data Collection:
Three bags of M&M’s and three cups were used. One bag of M&M’s was open and the number of each colour was counted and recorded. This was repeated for the other two bags of M&M’s. A ratio of each colour to the total number in the cup was made. The total number of each colour was found and recorded. A ratio of each colour to the total number of M&M’s was calculated and recorded. All observations were recorded in a table and used to create a bar chart. The experiment was repeated for accuracy.
The theoretical probability was calculated by dividing the number of M&M’s in each bag by the total number of colours. This method was use to determine how much of each colour would hypothetically be in each bag if all the colours were even. The theoretical probability calculated shows that for each bag there should be approximately 9-10 M&M’s of each colour in each bag. However, this was not the case. As shown in the results, all but one was not near the theoretical probability as seen in Table 2. For the overall the theoretical probably should be approximately be 29 of each colour in total. The probability of each colour overall was found to be as follows:
TotalRed 19/172Blue 39/172Green 26/172Brown 15/172Orange 43/172Yellow 30/172
However it was found that only green colour green was close to the theoretical. Considering that, Standard deviation is was the value calculated to indicate the extent of deviation for a group as a whole for each bag and all together. In theory, calculating the standard deviation would prove that the probability of each colour of M&M’s in each cup is “off” and by how much. If the distribution is not even the standard deviation would not be zero. My theory is the standard deviation would illustrate that with the larger data the deviation would be closer to zero as the theoretically probability of any different colours are closer in larger amounts of data.
Based on the calculations, the standard deviations observed did not support my theory of the standard deviation being close to zero but it supported the theory that there was not even distribution of M&M’s. It was expected that larger data would be closer to zero, however this was not the case. It appears as though the data was still too far away from the theoretical probability due to the combine amounts of data being too far away from the theoretical value. However, the deviations of cup 1 and 3 were somewhat similar as a result of cup 1 and 3 have the same number of M&M’s in their cups. Cup 2 had the smallest deviation as the number for each colour was closer to the
The proportions of each colour in each bag of M&M’s were found to be uneven. The standard deviation of Cup 1, 2 and 3 were 5.41, 2.71 and 4.18 respectively. This experiment was relatively simple; however, the mathematical methods used did not yield the expected results. Although the experiment was not successful, reviewing has made clear some of the factors that may have contributed to the unsuccessfulness; •The bags of M&M’s not having the same distribution in each varied the deviations as cup 2 was no where near the deviation of cup’s 1 and 3 •The combined number of data as mentioned earlier was being too far away from the theoretical probability for the overall total.