As essential ingredient in the Mendelian hypothesis is that the choice of which allele passed to a gamete is
made at random, hence, two alleles of a pair enter any gamete with equal probability. Also, the gametes of
two different mating types are combined in the same random manner through the process of fertilization.
One of the assumptions in Mendelian inheritance is that during fertilization male gametes combine with
female gametes independently of any alleles that they carry. Fixed probabilities, then, can be applied to
such events as meiosis and fertilization when conducting genetic analysis.
Using the basic rules for elementary probability theory, combinations of event in Mendelian genetics
can be calculated. The two types of combinations most often encountered are those events given as (1)
mutually exclusive and (2) independent. Mutually exclusive means that the occurrence of one event excludes
the possibility of the others. Whenever such alternative possibilities exist for the satisfaction of a genetic
problem, the individual probabilities are combined by addition. For example, the probability of obtaining the
dominant phenotype from a Gg x Gg cross is 3/4. Thus result is due to the addition of 1/4 (the probability for
GG) and 1/2 (the probability for Gg). The combined probability in this case is the product of the individual
probabilities. Since the genotype of any particular progeny will be the result of combining the alleles of the
gametes from the two parents, proportions of the different genotypes will be the product of the individual
gamete proportions. For example, in the cross Gg x Gg,
Maternal Gg →
gametes 1/2 G and 1/2 g
Paternal Gg →
gametes 1/2 G and 1/2 g
The probabilities of the genotypes are derived by multiplying the individual gamete probabilities in all
combinations, maternal with paternal.
1/2 G x 1/2 G = 1/4 GG
1/2 G x 1/2 g = 1/4 Gg
1/2 g x 1/2 G = 1/4 Gg
1/2 g x 1/2 g = 1/4 gg
and 1/4 Gg + 1/4 Gg = 1/2 Gg