# Microscopic Toolmark Analysis

I am conducting research on microscopic toolmark analysis. If I have a toolmark with 27 striations (lines) of varying spatial relationships (orientations), widths and densities, do I use the combination formula to determine the probablity that another toolmark will by chance have a group of at least eight consecutively matching striations: that is the striae have the same spatial relationship, the same density(shades of gray), and the same width. I have done this calculation with the combination formula to determine the probability of having 8 striae out of 27 from one toolmark matching another set of 8 striae out of 27 in a second toolmark in spatial relationship only. My answer was 1/2,200,000. Using probability, I determined that the chance of 8 striae matching in density is 2 to the 8th power (this is assuming that the striae either did or did not match in density or shades of gray),which equals 256. I then multiplied the 1/2,200,000 x 256 to obtain 1/568,000,000: the probablity that 8 striae out of the 27 will match in spatial relationship and density. Lastly, I used 2 to the 8th power, 256, as the value for two striae randomly matching in width. Then I multiplied 1/568,000,000 x 256 to obtain 1/145,000,000,000: the chance that 8 striae out of 27 will match in spatial relationship, density, and width. Is this correct or should I have done this calculations differently? Second, how would I determine the chance of having two separate groups of five consecutively matching striae? Thanks for your help

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... the striae either did or did not match in density or shades of gray),which equals 256. I then multiplied the 1/2,200,000 x 256 to obtain 1/568,000,000: the probablity that 8 striae out of the 27 will match in spatial relationship and density. Lastly, I used 2 to the 8th power, 256, as the value for two striae randomly matching in width. Then I multiplied 1/568,000,000 x 256 to obtain 1/145,000,000,000: the chance that 8 striae out of 27 will match in spatial relationship, density, and width. Is this correct or should I have done this calcualtions differently? Second, how would I determine the chance of having two separate groups of five consecutively matching striae? Thanks for your help

Solution:

Your answer is correct with a bit error of your calculation, the reasoning is as follows:

Take a simple example of 5 ...