If A and B must occur in order to bring about outcome C, then the probability of 
In contrast, if an outcome depends on the occurrence of any one of several mutually exclusive alternatives, then the probability of the outcome is obtained by adding together the probabilities of the alternatives. This is the or rule of probability:
If A or B must occur to get outcome C, then the probability of 
As an example, we can calculate the probability of getting an
11 when rolling two dice, die A and die B. In order to roll an 11, we need a
5 and a
6. The probability of rolling a
5 on die A and a
6 on die B is
But we can also roll an
11 with a
6 on die A and a
5 on die B. This is a mutually exclusive alternative to the first roll we considered; its probability is also
1/ 36. Since either A
5, B
6 or A
6, B
5 gives us a total of
11, the final probability of rolling an
11 using two dice is
1 /36 + 1/36 = 2/36 = 1/18.
Moving from gambling to genetics, we can calculate the probability that a cross between genotypes AABBCc and aaBbCc will produce an offspring with genotype AaBbcc. Taking one gene at a time, the probability of the Aa combination is a perfect 1, since an AA and aa cross can produce only Aa offspring.
The probability of the Bb combination is 1/2, because the BB and Bb cross will produce Bb offspring 50 percent of the time.
The probability of the cc combination is 1/4, because the Cc and Cc cross gives cc offspring 25 percent of the time.
Since Aa
and Bb
and cc must occur to produce our desired outcome, the probability is
Test Crossing (Back Crossing)
A test cross is the means by which a scientist can determine whether an individual with a dominant phenotype has a homozygous (AA) or heterozygous (Aa) dominant genotype. The test cross involves mating the individual with the dominant phenotype to an individual with a recessive (aa) phenotype and observing the offspring produced. If the individual being tested is homozygous dominant, then all offspring will have a dominant phenotype, since all the offspring will have at least one A allele and the A is dominant.
If the tested individual is heterozygous dominant, then half of the offspring will show the dominant phenotype, while the other half show the recessive phenotype.
Incomplete Dominance and Codominance
Mendel’s law of dominance is generally true, but there are many exceptions to the law. In some instances, instead of a heterozygote expressing only one of two alleles, both alleles could be partially expressed. For example, the flower color of the four o’clock plant is determined by a single gene with two alleles: plants homozygous for the R1 allele have red flowers, while plants homozygous for the R2 allele have white flowers. If interbred, the heterozygous R1R2 plants have pink flowers. Incomplete dominance is the term used to describe the situation in which the heterozygote phenotype is intermediate between the two homozygous phenotypes.
