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Problem 3. Eye colour is determined by a single gene, and each individual has two copies of the gene. For simplicity, we assume there are only blue and brown eyes. If both genes of an individual are blue, they have blue eyes; Otherwise they have brown eyes. (In technical terms, blue eyes are recessive and brown eyes are dominant.) A child inherits randomly one copy of the gene from each parent. (See e.g. season 4 of The bridge for the significance of these facts.) (a) Suppose Fanny and her parents have brown eyes but her brother Alexander has blue eyes. What is the conditional probability that Fanny has two brown genes? b) Suppose Fanny has 3 children with Lars, who has blue eyes, and all 3 have brown eyes. What is the conditional probability of the same event?

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