Several studies have found that the first-born child in a family is more prone to allergies like hayfever than younger children in the family. In fact, the probability that a first-born suffers from hayfever is about twice the probability that a later-born child suffers from hayfever. This is thought to happen because later-born children are likely to catch early childhood infections from their older siblings, making their immune systems more robust to allergens.

In New Zealand, about 40% of people are first-borns.

a. Define a suitable sample space, along with events H and F describing whether a person suffers hayfever and whether they are the first-born in their family. Write out all the information in the question in the form of probability statements.

b. For your defined population, find the probability that a person with hayfever is a first-born.

c. Given the additional information that 13% of New Zealanders suffer from hayfever, find:

i. the probability that a first-born has hayfever, and ii. the probability that a later-born has hayfever.