Question

In a farm animal breeding programme, the animal with the dominant A phenotype, the recessive b phenotype, the dominant D phenotype, and the recessive e phenotype are commercially important. The inheritance of these traits follows Mendelian laws. From the tetra-hybrid cross of two genotypes AaBbDdEe and AaBbDdEe, the expected frequency of offspring that will show all the above-mentioned desired phenotypes is ................... (rounded off to 3 decimals)

Hint:

To calculate the probability of multiple desired traits, multiply the individual probabilities for each trait's phenotype, considering whether the trait is dominant or recessive.

Answer 1

Step 1: Identifying the inheritance pattern.
We are dealing with a tetra-hybrid cross, which involves four traits (A, B, D, and E) with two alleles each. The genotypes of the parents are AaBbDdEe. The desired phenotypes for each trait are:
- \( A \) = dominant phenotype
- \( b \) = recessive phenotype
- \( D \) = dominant phenotype
- \( e \) = recessive phenotype
Step 2: Calculating probabilities for each trait.
- For the A trait: \( Aa \times Aa \) cross gives a probability of \( \frac{3}{4} \) for offspring with dominant \( A \).
- For the b trait: \( Bb \times Bb \) cross gives a probability of \( \frac{1}{4} \) for offspring with recessive \( b \).
- For the D trait: \( Dd \times Dd \) cross gives a probability of \( \frac{3}{4} \) for offspring with dominant \( D \).
- For the e trait: \( Ee \times Ee \) cross gives a probability of \( \frac{1}{4} \) for offspring with recessive \( e \).
Step 3: Calculating the overall probability.
The overall probability of obtaining the desired phenotypes is the product of the probabilities for each individual trait: \[ P(\text{desired offspring}) = \left( \frac{3}{4} \right) \times \left( \frac{1}{4} \right) \times \left( \frac{3}{4} \right) \times \left( \frac{1}{4} \right) \] \[ P(\text{desired offspring}) = \frac{3}{4} \times \frac{1}{4} \times \frac{3}{4} \times \frac{1}{4} = \frac{9}{256} = 0.035 \] Final Answer: \[ \boxed{0.035} \]