Given a Peptide Array with region R of l columns and w rows, what is the probability that a randomly selected l * r region is indicative of contamination?
- Possible contamination is defined as x positive luminescent data values within a total possible number of values t.
- Contamination is defined as N successive positive Bernoulli trials of possible contamination regions. For example, out of a possible 10 tested regions, if 9 are positive, then this is considered contamination
N = Number of tested regions, where each tested region is defined as a Bernoulli trial r = success, where success is defined as above a contamination threshold p = probability of contamination, for example, 4 positive luminescent values within a total possible 10 values would be 4/10 = 0.4 r = probability of no contamination, following the example for p, 1 - 0.4 = 0.6 P = Probability of contaminated region
P = (N!)/(r!(N-r)!) * p^r * q^(N-r)
If the threshold to identify a contaminated region of the array is exactly r successes for N possible trials, then use
p^r * q^(N-r)
Note that N!/(r!(N-r)! will equal 1 in this scenario
If the threshold to identify a contaminated region of the array is at least r successes in N possible trials, then use:
P = (N!)/(r!(N-r)!) * p^r * q^(N-r)
For example, if the a region R has 20 possible values, and if at least 4 are positive within this region determines possible contamination, and if 4 out of 5 successive tests determine contamination, then the probability of having a contaminated plate is:
p = 4/20
q = 16/20
N = 5
r = 4
P = (5!)/(4!(1!)) * (0.2)^4 * (0.8)^1 = 0.0064