The total number of genotypes and phenotypes in a dihybrid test cross

A dihybrid test cross is a genetic cross between an individual that is heterozygous for two different traits with an individual that is homozygous recessive for those traits. This type of cross is used to determine the genotype of the heterozygous individual and to study the inheritance of two different traits simultaneously.

Genotypes in a dihybrid test cross
In a dihybrid test cross, the heterozygous individual is crossed with a homozygous recessive individual for both traits. Let's assume that the heterozygous individual has the genotype AaBb, where A and B represent dominant alleles and a and b represent recessive alleles. The homozygous recessive individual will have the genotype aabb.

When these two individuals are crossed, the possible genotypes of the offspring can be determined by using the principles of Mendelian genetics. Each parent can contribute one allele for each trait, resulting in the following possible genotypes:

- AB (homozygous dominant for both traits)
- Ab (heterozygous for the first trait, homozygous recessive for the second trait)
- aB (homozygous recessive for the first trait, heterozygous for the second trait)
- ab (homozygous recessive for both traits)

Therefore, there are four possible genotypes in a dihybrid test cross.

Phenotypes in a dihybrid test cross
Phenotypes are the observable characteristics or traits displayed by an organism. In a dihybrid test cross, the phenotypes are determined by the expression of the dominant or recessive alleles for each trait.

Assuming that the dominant alleles (A and B) result in a particular phenotype, while the recessive alleles (a and b) do not, the possible phenotypes in the offspring can be determined:

- Phenotype 1: Both traits show the dominant phenotype (AB) - individuals will display both traits.
- Phenotype 2: Only the first trait shows the dominant phenotype (Ab) - individuals will display the first trait but not the second.
- Phenotype 3: Only the second trait shows the dominant phenotype (aB) - individuals will display the second trait but not the first.
- Phenotype 4: Both traits show the recessive phenotype (ab) - individuals will not display either trait.

Therefore, there are four possible phenotypes in a dihybrid test cross.

Summary
In a dihybrid test cross, there are four possible genotypes and four possible phenotypes. The genotypes include homozygous dominant for both traits (AB), heterozygous for the first trait and homozygous recessive for the second trait (Ab), homozygous recessive for the first trait and heterozygous for the second trait (aB), and homozygous recessive for both traits (ab). The phenotypes are determined by the expression of the dominant or recessive alleles for each trait, resulting in the expression of both traits, only the first trait, only the second trait, or neither trait.

Answer is 4 phenotypes and 9 genotypes.

for that follow this rule:(for genotypes)

we know that, for monohybrid cross
genotypic ratio is 1:2:1

then to get it for a di hybrid cross, simply do.
this:

monohybrid: 1:2:1
/ | \
1:2:1:2:4:2:1:2:1
|
this is doubled