# Are the colours of M&M’s evenly distributed in a bag of M&M’s? Sample

Table of Content

Purpose of Project / Aim:

Probability is an educated idea or conjecture to find if a peculiar event will happen. Probability is of import to help in doing and foretelling mundane determinations ; the chance that a kid will be born with reaping hook cell disease or the chance that harvests will decease are all of import for the human endurance. The usage of M & A ; M’s is to replace for the illustrations listed above to analyze chance sing they are used in mundane life and are hence readily accessible. When persons consume M & A ; M’s. they indentify peculiar colorss and this can be related to chance. Calculating the chance of a peculiar coloring material is chiefly based on the entire figure of M & A ; M’s you have and how much of that coloring material is present. This is because the general expression for chance is involvement over the entire: P ( A ) = The Number Of Ways Event A Can Occur

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The entire figure Of Possible Results

Standard divergence is the value calculated to bespeak the extent of divergence for a group as a whole. Standard divergence will be used to help with the analysis of this experiment. This experiment aims to find whether the parts of each coloring material in each bag of M & A ; M’s are even by finding the chance of picking a peculiar coloring material and if non by how far “off” they are.

Method of Data Collection:

Three bags of M & A ; M’s and three cups were used. One bag of M & A ; M’s was unfastened and the figure of each coloring material was counted and recorded. This was repeated for the other two bags of M & A ; M’s. A ratio of each coloring material to the entire figure in the cup was made. The entire figure of each coloring material was found and recorded. A ratio of each coloring material to the entire figure of M & A ; M’s was calculated and recorded. All observations were recorded in a tabular array and used to make a saloon chart. The experiment was repeated for truth.

The theoretical chance was calculated by spliting the figure of M & A ; M’s in each bag by the entire figure of colorss. This method was usage to find how much of each coloring material would hypothetically be in each bag if all the colorss were even. The theoretical chance calculated shows that for each bag there should be about 9-10 M & A ; M’s of each coloring material in each bag. However. this was non the instance. As shown in the consequences. all but one was non near the theoretical chance as seen in Table 2. For the overall the theoretical likely should be about be 29 of each coloring material in entire. The chance of each coloring material 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 merely green coloring material viridity was near to the theoretical. Sing that. Standard divergence is was the value calculated to bespeak the extent of divergence for a group as a whole for each bag and all together. In theory. ciphering the standard divergence would turn out that the chance of each coloring material of M & A ; M’s in each cup is “off” and by how much. If the distribution is non even the standard divergence would non be nothing. My theory is the standard divergence would exemplify that with the larger informations the divergence would be closer to zero as the theoretically chance of any different colorss are closer in larger sums of informations.

Based on the computations. the standard divergences observed did non back up my theory of the standard divergence being close to zero but it supported the theory that there was non even distribution of M & A ; M’s. It was expected that larger informations would be closer to zero. nevertheless this was non the instance. It appears as though the information was still excessively far off from the theoretical chance due to the combine sums of informations being excessively far off from the theoretical value. However. the divergences of cup 1 and 3 were slightly similar as a consequence of cup 1 and 3 have the same figure of M & A ; M’s in their cups. Cup 2 had the smallest divergence as the figure for each coloring material was closer to the

Decision:

The proportions of each coloring material in each bag of M & A ; M’s were found to be uneven. The standard divergence of Cup 1. 2 and 3 were 5. 41. 2. 71 and 4. 18 severally. This experiment was comparatively simple ; nevertheless. the mathematical methods used did non give the expected consequences. Although the experiment was non successful. reviewing has made clear some of the factors that may hold contributed to the unsuccessfulness ; •The bags of M & A ; M’s non holding the same distribution in each varied the divergences as cup 2 was no where near the divergence of cup’s 1 and 3 •The combined figure of informations as mentioned earlier was being excessively far off from the theoretical chance for the overall sum.