Table S4.

Probability of a Nanowell (in an array of 25,600) containing at most one cell

No. of cells seeded into single nanowell	Probability of a well containing at most one cell, %
100	99.99
500	99.98
1,000	99.93
2,000	99.71
3,000	99.36
4,000	98.90
5,000	98.32
10,000	94.09

Consider the case of distributing n cells among m wells in a Nanowell array. For large values of m and n, the number of cells in a given Nanowell can be described by a Poisson random variable X. Then the probability that a given Nanowell contains at most one cell is given by the following:

$$X\sim \mathrm{Pois}\left(\frac{n}{m}\right),$$

$$P\left(X-\kappa \right)=\frac{1}{\kappa !}{\left(\frac{n}{m}\right)}^{\kappa }\exp \left(-\frac{n}{m}\right),$$

$$P\left(X\mathrm{\le }1\right)=P\left(X=0\right)+P\left(X=1\right)=\left(1+\frac{n}{m}\right)\exp \left(-\frac{n}{m}\right).$$