3. Flower Breeding
Solution:
The Bayesian network：
NPT for Plant_1_Genotype、Plant_2_Genotype、Plant_3_Genotype node（the same values of these）:
NPT for Flower_Colour（the same values of all plants）:
NPT for Offspring_1_Flower_Colour、Offspring_2_Flower_Colour（the same values of all plants）:
Inserting the evidence into the Bayesian network:
Result:P(red flowers|the second generation offspring) = 66.7%
4. Horse Stud
Solution:
Because the frequency of occurrence of the recessive gene is 1 in every 100 horses for the horses without a recorded father or mother:
P(AA| the horse without a recorded father or mother) = 99%
P(Aa| the horse without a recorded father or mother) = 1%
The Bayesian network:
NPT for the first generation horses(Mike、Cecily、Brain、Jill、Jack) genotype nodes:
NPT for the first generation horses(Gwenn、Eric、Dorothy、Fred) genotype nodes:
Inserting the evidence(P(AA|Fred)=100%、P(Aa|Irene)=100%、P(Aa|Henry)=100%) into the Bayesian network:
Result: Brain、Eric、Dorothy should be culled from breeding program.