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.