[SOLVED] Probability problem

Hi,

Can anyone offer any tips for solving the following question:

Haemochromatosis is a genetic disorder that causes people to absorb excessive amounts of dietary iron. The genetic model for its transmission is as follows. The genotype aa is diseased, the genotype Aa is not diseased but is a carrier, the genotype AA is neither diseased nor a carrier. When two people mate, each contributes one of their genes (A or a), with probability 0.5.

(a) Write down the probability distribution of the genotype of the offspring when two carriers mate.

(b) The distribution of genotypes in the general population is P(AA)=p, P(Aa)=q, P(aa)=r. If a carrier mates with someone of unknown genotype, write down the probability distribution of the genotype of the resulting off-spring.

(c) If a couple are both carriers and have five children, write down an expression, which gives the probabilities of different numbers of children having the disease. What is the probability that more than three of the children will have the disease?

(d) Suppose a class of 100 students has the following distribution of genetic types.

Genetic type AA aA aa

No. of students 75 20 5

If six students are selected at random for testing, write down an expression for the probability that two students of each genetic type will be selected.

(e) A general practitioner receives requests for screening for haemochromatosis at a rate of 3 per week. The pattern of such requests may be modelled by a Poisson probability distribution, with parameter λ = 3. Write down an expression for the probability that in any one week more than five such requests will be made?

Also I'd be very grateful if anyone can recommend a good introductory college probability/stats book with lots of worked examples. I'm struggling to get my head arounds these problems and my notes are not helping much!

Thanks.

**Edit by the OP:** Solved