Constrained Survey to Venn Diagram

5. A group of 100 students are asked if they like folk music, rock music or soul music. \begin{displayquote} All students who like folk music also like rock music No students like both rock music and soul music 75 students do not like soul music 12 students who like rock music do not like folk music 30 students like folk music

1. Draw a Venn diagram to illustrate this information.
2. State two of these types of music that are mutually exclusive. \end{displayquote} Find the probability that a randomly chosen student
3. does not like folk music, rock music or soul music,
4. likes rock music,
5. likes folk music or soul music. Given that a randomly chosen student likes rock music,
6. find the probability that he or she also likes folk music.

1. Hugo recorded the purchases of 80 customers in the ladies fashion department of a large store. His results were as follows

20 customers bought a coat
12 customers bought a coat and a scarf
23 customers bought a pair of gloves
13 customers bought a pair of gloves and a scarf no customer bought a coat and a pair of gloves 14 customers did not buy a coat nor a scarf nor a pair of gloves.

1. Draw a Venn diagram to represent all of this information.
2. One of the 80 customers is selected at random.
   1. Find the probability that the customer bought a scarf.
   2. Given that the customer bought a coat, find the probability that the customer also bought a scarf.
   3. State, giving a reason, whether or not the event 'the customer bought a coat' and the event 'the customer bought a scarf' are statistically independent. Hugo had asked the member of staff selling coats and the member of staff selling gloves to encourage customers also to buy a scarf.
3. By considering suitable conditional probabilities, determine whether the member of staff selling coats or the member of staff selling gloves has the better performance at selling scarves to their customers. Give a reason for your answer.

5. A person's blood group is determined by whether or not it contains any of 3 substances \(A , B\) and \(C\). A doctor surveyed 300 patients' blood and produced the table below.

1. Draw a Venn diagram to represent this information.
2. Find the probability that a randomly chosen patient's blood contains substance \(C\). Harry is one of the patients. Given that his blood contains substance \(A\),
3. find the probability that his blood contains all 3 substances. Patients whose blood contains none of these substances are called universal blood donors.
4. Find the probability that a randomly chosen patient is a universal blood donor.