Discuss the following:
Your firm has classified orders as either large or small in dollar amount and as either light or heavy in shipping weight. In the recent past, 28% of orders have been large dollar amounts, 13% of orders have been heavy and 10% of orders have been large in dollar amounts and heavy in weight.
a. Complete a probability tree for this situation, with the first branch being the event "large dollar amount".
b. Construct the joint probability table for this situation.
c. Draw a Venn diagram for this situation.
d. Find the probability that an order is large in dollar amount or heavy (or both).
e. Find the probability that an order is for a large dollar amount and is not heavy.
f. Of the orders with large dollar amounts, what percentage are heavy? What conditional probability does this represent?
g. Of the heavy orders, what percentage are for large dollar amounts? What conditional probability does this represent?
h. Are the events "large dollar amount" and "heavy" mutually exclusive? How do you know?
i. Are the events "large dollar amount" and "heavy" independent? How do you know?