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DNA STUDY
The Calculator shows the most likely number of mutations for any given set of markers, generation gap and average mutation rate. The formula uses a standard probability mechanism, which looks more complicated than it actually is :
Where :
P = the mutation rate (eg quoted as 0.0033 and not a percentage at 0.33)
T= the total number of markers tested multiplied by the number of generations x the number of people in the comparison
t = the number of markers that have mutated
! = factorial, for example 6! is the as 6x5x4x3x2x1
To work out the probability of 2 mutations in 44 markers over 7 generations, between 2 people using a mutation rate of 0.33%:
P = 0.0033
T = 44 x 7 x 2 = 616
t = 2
Plugging the numbers in to the equation :
= (1-0.0033)^(616-2) x 0.0033^2 x (616!/614!)/2!
= 0.131394 x 0.00001089 x (616x615)/(2x1)
= 0.271 or 27.1%
Note that if you try to calculate 616!, your calculator or computer will find this number to big to handle. We used a short cut above used to calculate 616!/614!, which is the same as 616x615. To calculate 64!/60!, this is the same as 64 x 63 x 62 x 61. Don’t bother with long hand however, just use the Calculator. Below is an example of 2 people being compared over 4 generations, comparing 63 markers and using a mutation rate of 0.0041, or 0.41%. (a screen shot is below). There are 504 opportunities to see a single mutation and the most likely outcome is to see 2 mutations, at a 27% chance.
Calculator
