A particular diagnostic test performs such that when an individual has the disease, a positive result will occur 97.1%, whereas an individual without the disease will show a positive result 2.0% of the time. The prevalence of infected persons in the general population is known to be 1 in 1500. An epidemiological study has identified that the probability of an infected person transmitting the disease to a close contact is 4.7% for contacts with no pre-existing health conditions, and 10.7% for contacts with pre-existing health conditions. i. What is the probability that an individual actually has the disease, if they have been tested and the result is positive? Show your reasoning. ii. In a family home with 10 relatives, what is the likelihood that a specific family member with pre-existing conditions contracts the disease by direct contact with another family member? Show your reasoning.