An Explanation of Binomial Distribution

We can use statistical theory to find the probability of a certain number of successful events out of a small, finite number of trials. With a very large number of offspring, the distribution of zygotes will approach 1/4BB: 1/2 Bb: 1/4 bb. However, due to small sample size, the relative frequency of each type of offspring may not be the expected 1:2:1 ratio.

Example

Assume complete dominance gene action so that we cannot distinguish BB from Bb genotypes. Now we have only two classes of offspring or two outcomes: B_ or bb. We can add the probability of BB and Bb to get the probability of B_. P (BB) + P (Bb) = 1/4 + 1/2 = 3/4, because these two events are mutually exclusive.

We can imagine that with a very large number of offspring, 3/4 would be B_ and 1/4 would be bb genotypes. 3 B_: 1 bb is our expectation. What if we only have a small number of offspring? Due to sampling, we might have some families that consist only of bb offspring or only of B_ offspring. The larger the family size, the less likely that we would have only bb offspring. We can use the binomial distribution to calculate the probability of all bb offspring in a family of size n, when n is a small number.