All textbooks describe the segregation resulting from the selfing or F1 crosses of plants or animals heterozygous for two traits as giving progeny in a 9:3:3:1 ratio according to their phenotypes. Mendel never described the ratio of progeny from plants heterozygous in two genes in this way. Instead he selfed the progeny from the heterozygotes and classified them into three categories. The first category contained plants that were homozygous for both traits (there were four types of plants, each represented 1X in the population), the second had plants that were heterozygous for one of the traits (again there were four types of plants, but each was represented 2X in the population), and the third were plants that were heterozygous for both traits (one group, representing 4x in the population). Using a Punnett Square, show the equivalence of these results with the more familiar 9:3:3:1 ratio.
In describing the results of the independent assortment of three traits, Mendel says that 54/64 of the plants will express at least two of the dominant traits. Demonstrate that this is true.
Two children of normal-appearing parents both have a genetic disease. The first suffers from cystic fibrosis, while the second has albinism. Both conditions are autosomal. What is the probability that the next child in the family will be normal in both respects?
Mendel's paper has been so important that people have looked at every aspect with extreme care. This examination came to the conclusion that some of Mendel's data were too good; that he could not have gotten the results he did. The specific argument is that he should not have gotten the 2:1 ratios of self progeny from the F2 parents expressing a dominant trait. In his experiments Mendel took 10 pea seeds from each heterozygous plant and looked at what they became.
What is the probability that an F2 plant showing the dominant phenotype will produce some seeds that will grow into plants with the recessive phenotype?
What is the probability that a single seed from a heterozygous F2 plant will give a plant with the dominant phenotype?
What is the probability that two seeds from a heterozygous plant will give plants with the dominant phenotype? (Remember that the probability of both of two events occurring is calculated by multiplying the probability of each event)?
What is the probability of all ten of the seeds from a heterozygous F2 plant resulting in plants with the dominant trait?
The number you derived in Part d represents the number of F2 heterozygotes that Mendel should have misjudged as being homozygous for the dominant trait (because he looked at too few seeds). Using this value, calculate the ratio that Mendel should have obtained rather than getting a 1:2:1 ratio.
My daughter likes to say that she is 1/4 Danish because both of the parents of her maternal grandmother came from Denmark. Lots of people (and several horrendous laws in the past) also made statement like this, but are they true?
Imagine a male/female species with only two pairs of chromosomes (to make the problem easier the species has no recombination and the chromosomes are not different in the two sexes). What is the probability that either chromosome from one of the grandparents will be inherited in a grandchild?
(Extra) What percentage of human granddaughters would have approximately half (11 or 12) of the 23 chromosomes from their maternal grandmothers? Assume that no recombination occurs. (Hint: using the binomial expansion will help with the calculation.)
At a reunion of a family that can trace its ancestry in the United States to the late 1600s, two men see someone that reminds them of their Uncle Bill (now deceased). They talk to this apparent lookalike and find that the closest common ancestor between him and Uncle Bill lived two hundred years ago. They wonder whether their family has some very strong traits (to use their term; they are a very proud family). Give several explanations (some genetic, some not) for how Uncle Bill and this individual could look alike.