An Explanation of Binomial Distribution Part II
Example
Let P (B_) = 3/4; P (bb) = 1/4; n = 4 which is the
family size; r = o which is the number of Bb offspring
or successful events.
The binomial distribution is:
This formula will tell us the probability of r ‘successful’
events out of a total of n events. We will define p
as the probability of a ‘success’ and q as the probability
of a ‘failure’. p + q = 1 and n = r + (n-r).
In our example we have a family size of 4 or 4 events,
n = 4. We want to find the probability of r = o or zero
successes and 4 failures. Four offspring of the bb genotype
is the equivalent of four failures and the probability
of each individual failure = 1/4. P (event) = P (families)
family size = 4, = # of trials. We are expanding the
binomial expression (p+q)4.
n!
= 4 x 3 x
2 x 1 = 24
r! =
0! = 1
(n-r)!
= (4-0)! = 4! = 24
| n! |
pr qn-r = (1)(3/4)0(1/4)4 |
| r!(n - r)! |
Our expectation is that the proportion of families
of size 4 which contain four bb offspring is 1/256.
