In a recent study, it is found that a person in a city has a 40% chance of being infected by the flu virus. 20% of those who have been infected with the virus are symptoms free while 10% of those who are not infected show the symptoms. i) Draw a tree diagram to summarize the above information and label all necessary information, including the intersection probabilities.

Let $I$ be the event that a person is infected by flu virus. Its probability is $p(I)=0.4$. $I'$ is the event that a person is not infected with its probability, $p(I')=1-p(I)=1-0.4=0.6$

Let $S$ be an event representing a person showing signs and $S'$ is the event that an individual is symptoms free.

We are given the following conditional probabilities.

$p(S'|I)=0.20\\p(S|I')=0.10$

We can represent these information in the tree diagram below. The respective intersection probabilities are indicated on the right of the tree diagram