Your company maintains a database with information on your customers, and you are interested in analyzing patterns observed over the past quarter. In particular, 23% of customers in the database placed new orders within this period. However, for those customers who had a salesperson assigned to them, the new order rate was 58%. Overall, 14% of customers within the database had salespeople assigned to them.
a. Draw a probability tree for this situation.
b. What percentage of customers in the database placed a new order but did not have a salesperson assigned to them?
c. Given that a customer did not place a new order, what is the probability that the customer had a salesperson assigned to him or her?
d. If a customer did not have a salesperson assigned to him or her, what is the probability that the customer placed a new order?