Three naturally occuring varieties of sweet pea have purple, red and white flowers. The flower colors may be assumed to be determined by two genes. The first gene has two alleles: R and r. A sweet pea with one or more R alleles will have red flowers. The second gene also has two alleles: P and p. a sweet pea with one or more P alleles will have purple flowers. If the sweet pea's alleles are rr and pp the flowers will be white.

Let x denote the proportion or R alleles for the first gene amonsst all the sweet peas cultivated in a particular garden centre, with 1-x the proportion of r alleles; let y similarly represent the proportion of P alleles, 1-y the propprtion of p alleles.

(i)Calculate, in terms of x & y, the prrobability that a random selected sweet pea from the garden cenntre has (i) purple flowers, (ii) red flowers, (iii) white flowers.

(ii) Given that 11.64% of the seet peas in the garden centre have red flowers and 23.01% have purple flowers, calculate the values of x and y.

(iii) A sweet pea with purple flowers is selceted at random from the garden centre. What is the probability that it will have two P alleles?

(iv) The pollen from a sweet peas that has two P allels always carries the P allele, whereas the pollen from a sweet pea that has one P and one p allele has a 50/50 chance of carrying either allele. a species of bee visits only purple-flowered sweet peas: seeds that develop from pollination by such a bee carry one allele from the pollenand one from the plant which was pollinated. What is the probability that a seed of this type carries two P alleles?

D