1. You are a doctor with a patient who has received a positive mammogram. You want to estimate the probability that she actually has breast cancer before you talk to her. She is in a relatively low-risk group (age 45; overall, 0.8% (8 per 1,000) of women in this group have breast cancer). If she actually does have breast cancer, the probability is 90% that she will have a positive mammogram. If she does not have breast cancer, there is a 2% chance that she will nevertheless have a positive mammogram. What is the probability that this patient actually has breast cancer?

2. Galactosemia is a recessive human disease that is treatable by diet. Susan Smithers and her husband are both heterozygous for the galactosemia gene. If the couple has five children, what is probability that at least two of the children will have galactosemia?
What is the probability that exactly two of the children have galactosemia?

3. You have a generated a collection of mutant fruit fly strains such that each of them carries a single mutation and you want to find a mutation in your favorite gene, bravo. You have a reliable estimate that the chance of any given strain having a mutation in your favorite gene is 1/5,000. How many strains will you need to screen to be 90% sure that at least one will carry a mutation affecting your gene? How many to be 99% sure?

4. I notice a rare physical trait in one of my students that I suspect is genetic. I further suspect that it is recessive. To study this further, I find more people with this trait by advertising online. To simplify the analysis, I limit myself to families with exactly three children (my respondents each have two siblings). Assuming that the trait is autosomal, recessive and rare; and further assuming that my advertising has identified people with the trait at random, what fraction of the families do I expect to have 0/3 affected children, 1 affected child, 2 affected children and (all) 3 affected?