STAT/BIOST 550 B : Homework 1.

You can also find more information in the first powerpoint lecture: Chapter 1 part 1

1. In a population of pea plants, the frequency of the red-flower color allele (R) is 0.7 and the frequency of the white flower-color allele (r) is 0.3. The red allele (R) is dominant to the white allele (r).

(a) What is the probability that a pea plant has red flowers?
(b) What is the probability that a red-flowered plant has genotype RR?
(c) What is the probability that a red-flowered parent pea plant will pass on an R allele; an r allele?
(d) A pea plant with red flowers and known genotype Rr, is bred to a pea plant with red flowers and unknown genotype. What is the probability that these two plants will have an offspring that is RR; Rr; rr?

2. For the ABO blood types, the frequency of the A allele is 0.3, of the B allele is 0.1, and of the O allele is 0.6.
A person of blood type AB, and a person of blood type A but with an unknown genotype, have a child.
(a) In the population, what is the probability that a person will be AA, AO?
(b) What is the probability that the child of the two specified parents is AA, AB, BB, AO, BO, OO?
(c) The child is found to have blood type A. What is the probability that this child is AA, AO?
(d) If the child is AO, what is the probability that the parent of blood type A is AA, AO?

3. For the Cf gene, the allellic frequency of the normal allele is 0.975 and of the recessive mutant allele is 0.025.
Two people, who are phenotypically normal but have unknown genotypes, have a child.
(a) What proportion of phenotypically normal people are carriers?
(b) What is the probability that their child has Cf?
(c) Their child is phenotypically normal (i.e. does not have Cf). What is the probability that this child is a carrier?

4. The following comes from a real study, here at UW, and concerns typing of a family at a genetic marker locus with codominant alleles here labelled A, B, C and D.
An (untyped) couple have six kids. Three kids are typed and are all type BD. The other three are untyped, but have children.
(i) Untyped kid1, has spouse type AD, and 4 typed children, AB, BD, AB, and CD.
Question: if no errors, what type was kid1?
(ii) Untyped kid2, has spouse type AC, and two typed children, types AA and AC.
Question: if no errors, what can be said about the type of kid2?
(iii) Untyped kid3 and his untyped spouse have four typed children, types AC, BC, AD, and BC.
Question: what does this tell us about the types of kid3 and his spouse?

(a) Is there a problem with these data? Why?
(b) Is it more likely a pedigree error or a typing error? What additional information might help resolve that?
(c) Where is the error, most likely? Identify some possibilities.What additional information might help resolve that?