"Four traits that Mendel studied extensively in pea plants were flower position, seed color, stem length, and pod shape. For flower position, the axial (A) allele is dominant over terminal (a); for seed color, the yellow allele (Y) is dominant over green (y); for stem length, the tall (T) allele is dominant over dwarf (t); and for pod shape, the inflated (I) allele is dominant over constricted (i). If a test-cross was performed with a plant with the AAYyTtII genotype, what is the probability of observing an individual with the AayyTtIi genotype in the next generation

There is 1/4, or 25% of probabilities of observing an individual with the AayyTtIi genotype in the next generation.      

Explanation:

Available data:

Parental)    AAYyTtII     x     aayyttii

Gametes) AYTI, AyTI, AYtI, AytI

                 ayti

Punnet Square)         AYTI          AyTI        AYtI        AytI

                     ayti    AaYyTtIi   AayyTtIi  AaYyttIi   AayyttIi

There is 1/4, or 25% of probabilities of observing an individual with the AayyTtIi genotype in the next generation.

Note: If you do not want to perform the punnet square for the whole genotypes, you can make crosses for each gene and then multiply the corresponding probabilities to get the desired genotypic ratio. Like this:

Parental) AA   x   aa

Gametes) A   A   a   a

Punnet square)    A       A

                     a    Aa     Aa

                     a    Aa     Aa

There are 4/4 of probabilities of getting Aa genotype in the next generation

Parental) Yy   x   yy

Gametes) Y   y   y   y

Punnet square)    Y       y

                     y    Yy     yy

                     y    Yy     yy

There are 2/4 of probabilities of getting Yy genotype, and 2/4 of probabilities of getting yy genotype in the next generation

Parental) Tt   x   tt

Gametes) T   t    t   t

Punnet square)    T       t

                       t    Tt     tt

                       t    Tt     tt

There are 2/4 of probabilities of getting Tt  genotype, and 2/4 of probabilities of getting tt genotype in the next generation

Parental) II   x   ii

Gametes) I   I     i   i

Punnet square)    I     I

                       i    Ii    Ii

                       i    Ii    Ii

There are 4/4 of probabilities of getting Ii genotype in the next generation

The probabilities of observing an individual with the AayyTtIi genotype in the next generation is:

4/4 Aa  x   2/4yy   x   2/4Tt   x   4/4Ii

4/4 x 2/4 x 2/4 x 4/4 = 64/256 = 32/128 = 1/4

There are 1/4 or 25% of probabilities of observing an individual with the AayyTtIi genotype in the next generation            

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