To put the obvious first it's so clear that he meant 1/(3 * 10^7) that I'd have asked him straight out if it was a typo. If he insisted then I'd point out that 3 base pairs per codon for 10^7 codons is obviously 3*10^7 base pairs. If that didn't work I'd ask him to explain himself to find out just what absurdity he had in mind.
Looking at the thread:
quote:
It’s a Bernoulli Distribution.
P(Y) = Cn,y * p^y*q^n-y
y = number of success
n = number of tries
That works if the probabilities p and q are constant. Because he insists on mutations in 3 presumably different bases it isn't that simple. It can be used as an estimate, but there is a corrective factor that needs to be applied.
quote:
p -> We have three possible bases to change in each position, so the probability of mutating a specific base in a specific point is : 1/3^(10^7)
With the correction noted above this would be a reasonable probability if a "try" was a mutation. (i.e. if a mutation occurs, assuming equiprobability, the chance of it occurring at a particular location is 1 divided by the number of locations). Unfortunately he states:
A try is a reproduction event.The only moment when a mutation can happen and be passed on
In which case he should forget about the genome size and just use the per-base probability of mutation (a simpler calculation, since there is no need to invoke combinatorials)
Assuming that a "try" is a mutation:
[qs]
q -> 1 - p
so P( Y >= 3 ) = 1 - ( P(Y=0) + P(Y=1) + P(Y=2) )
[/quote]
The probability p is the probability of getting ONE specific mutation. But we don't want one specific mutation three times. We want 1 of three mutations, then one of the remaining two, then the last one (the order doesn't matter). SInce there are 6 ways that this could happen the real probability is about 6 times higher.
I estimate it as about 4*10-5 (if I did the calculation right). A simpler estimate (multiply the probability of one occurring by 10^6 and cube the result) comes out at about the same. The real probability ought to be a bit lower, but not greatly so.