A binomial distribution describes a population whose members take on only certain, discrete values. This is the case, for example, with the number of ^{13}C atoms in cholesterol because a molecule of cholesterol can have two ^{13}C atoms, but it can not have 2.5 atoms of ^{13}C. A population is continuous if its members may take on any value.

The probability of finding an atom of 13C in a molecule of cholesterol is given by the binomial distribution equation

where *P(X,N)* is the probability that an event will occur *X* times during *N* trials, and *p* is the event’s probability in a single trial. Carbon has two stable, non-radioactive isotopes, ^{12}C and ^{13}C, with relative isotopic abundances of, respectively, 98.89% and 1.11%.

Cholesterol has a chemical formula of C_{27}H_{44}O. To determine the probability of finding two atoms of ^{13}C in a single molecule of cholesterol, *P*(2,27), we take *X* as 2, *N* as 27, and *p* as 0.0111, obtaining a probability of 0.0033, or 0.33%. The figure below shows the binomial distribution through five atoms of ^{13}C.