Q.65 In a genetic cross between a true–breeding tall parent bearing red flowers and a
true–breeding dwarf parent bearing white flowers, only tall plants with red
flowers are obtained in the F1 population. Considering these two traits segregate
independently, if one tall individual is selected from the F2 population, the
probability that it would be genotypically homozygous for plant height and
make red flowers is __________ (Round off to two decimal places).
The probability is 0.14.
This dihybrid cross follows Mendel’s law of independent assortment, producing a classic 9:3:3:1 phenotypic ratio in F2. Selecting a tall plant from F2 requires conditional probability for the specific homozygous genotype.
Parental Cross
True-breeding tall red (TTRR) crossed with dwarf white (ttrr) yields all F1 as TtRr (tall red).
F1 self-cross (TtRr × TtRr) produces 16 equally likely F2 genotypes due to independent segregation of height (T/t) and flower color (R/r) loci.
F2 Phenotypic Ratios
- Tall plants: TT__ (4/16), Tt__ (8/16), tt__ (4/16) → Total tall = 12/16 = 0.75
- Red flowers: __RR (4/16), __Rr (8/16), __rr (4/16) → Total red = 12/16 = 0.75
- Tall red phenotype occupies 9/16 of F2 (T_R_ combinations).
Target Genotype
Required: TT for height (homozygous tall) and makes red flowers (R_, i.e., RR or Rr).
This excludes Tt (heterozygous height) and rr (white).
Qualifying genotypes (among 16 total): TTRR (1), TTRr (2) → 3/16 absolute probability.
Conditional Probability
Given selected plant is tall (probability space = 12/16):
P(TT and R_|tall) = P(TT and R_) / P(tall) = (3/16) / (12/16) = 3/12 = 0.25
“Make red flowers” means expresses red (R_), so height homozygous (TT) among tall plants.
Exact Calculation
- P(Tall) = 3/4
- TT and red (R_): TTRR (1), TTRr×2 (2) = 3 squares
- P = 3/12 = 0.25
F2 Punnett Square
| TR | Tr | tR | tr | |
|---|---|---|---|---|
| TR | TTRR | TTRr | TtRR | TtRr |
| Tr | TTRr | TT rr | Tt Rr | Tt rr |
| tR | TtRR | TtRr | ttRR | ttRr |
| tr | TtRr | Tt rr | ttRr | ttrr |
