Questions: What is the probability that the first offspring from this cross: At bb Dd Ee x AA bb DdEe will be a son with the genotype: AA bb Dd EE Type your answer as a decimal and round to 5 decimal places.

To determine the probability that the first offspring from the given cross will be a son with the genotype AA bb Dd EE, we need to consider both the genetic and sex determination aspects of the problem.

1. AA Genotype:

   • The cross is At bb Dd Ee (heterozygous for A) with AA bb Dd Ee (homozygous for A).
   • Probability of AA: The first parent can contribute either A or a, while the second parent can only contribute A.
   • Probability = 1/2 (A from first parent) * 1 (A from second parent) = 1/2.

2. bb Genotype:

   • Both parents are bb, so the offspring will definitely be bb.
   • Probability = 1.

3. Dd Genotype:

   • Both parents are Dd.
   • Probability of Dd: 1/2 (D from first parent) * 1/2 (d from second parent) + 1/2 (d from first parent) * 1/2 (D from second parent) = 1/2.

4. EE Genotype:

   • Both parents are Ee.
   • Probability of EE: 1/2 (E from first parent) * 1/2 (E from second parent) = 1/4.

• The probability of the offspring being male (son) is 1/2, assuming equal probability of male and female offspring.

The overall probability is the product of the probabilities for each independent event:

\[ \text{Probability} = \left(\frac{1}{2}\right) \times 1 \times \left(\frac{1}{2}\right) \times \left(\frac{1}{4}\right) \times \left(\frac{1}{2}\right) \]

\[ = \frac{1}{2} \times \frac{1}{2} \times \frac{1}{4} \times \frac{1}{2} \]

\[ = \frac{1}{32} \]

\[ = 0.03125 \]

Therefore, the probability that the first offspring will be a son with the genotype AA bb Dd EE is 0.03125.

Answer: 0.03125