Math 380
Spring 2023
Dr. Mary Ann Horn
Assignment 5
Due: Thursday, 9 March
1. In a certain village, 20% of the population has some disease. A test is administered which
has the property that if a person is sick, the test will be positive 90% of the time and if the
person is not sick, then the test will still be positive 30% of the time. All people tested positive
are prescribed a drug which always cures the disease but produces a rash 25% of the time.
Given that a random person has the rash, what is the probability that this person
had the disease to start with?
2. An insurance company considers that people can be split in two groups: those who are likely
to have accidents and those who are not. Statistics show that a person who is likely to have
an accident has probability 0.4 to have one over a year; this probability is only 0.2 for a person
who is not likely to have an accident. We assume that 30% of the population is likely to have
an accident.
(a) What is the probability that a new customer has an accident over the first year of his
contract?
(b) A new customer has an accident during the first year of his contract. What is the probability
that he belongs to the group likely to have an accident?
3. 46% of the electors of a town consider themselves as independent, whereas 30% consider
themselves democrats and 24% republicans. In a recent election, 35% of the independents, 62%
of the democrats and 58% of the republicans voted.
(a) What proportion of the total population actually voted?
(b) A random voter is picked. Given that he or she voted, what is the probability that the
person is independent? democrat? republican?
Exercises 2.1, 2.3, 2.5, 2.9 on pages 72 and 73 in the textbook by Anderson, Seppa?la?inen, and
Valko?.

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