The inheritance of horn growth in American cattle is determined by two genes. - One gene controls whether cattle have true horns; this gene is called the polled gene and has alleles P and p. Cattle that are homozygous recessive (pp) have true horns, while PP and Pp cattle lack true horns (i.e., are either polled or scurred). - One gene controls whether cattle are polled or scurred; this gene is called the scurred gene and has alleles Sc and Sn. The Sc allele confers scurring, - All cattle that are pp exhibit true horns, regardless of their genotype for the scurred gene. Thus, observing horned cattle is not informative for determining scurred genotype. - In male cattle, the Sc allele is dominant. Male cattle (that are PP or Pp) are scurred if they are genotypes ScSc or Scan; they are polled if they are genotype Snin. - In female cattle, the Sn allele is dominant. Female cattle (that are PP or Pp) are scurred if they are genotype ScSc; they are polled if they are genotype Scan or SnSn. Answer the following questions under the assumptions that 1) mating occurs independently of horn phenotype, 2) the polled gene and the scurred gene are inherited independently of each other, and 3) both genes follow the rules of Mendelian single-gene inheritance (alleles are inherited independently from each parent, with probability 0.50).c) Consider a mating between a polled American Holstein cow and a polled American Holstein bull, both of which were randomly selected from all American Holstein cattle. Young cattle are called calves (calf, singular) regardless of sex. i. What is the probability that a calf produced from this mating has true horns? ii. What is the probability that a calf produced from this mating has scurs? iii. Suppose that the first calf produced from this mating has scurs. What is the probability that the mother has the Scan genotype