A company receives shipments from two factories. Depending on the size of the order, a shipment can be in

1 box for a small order,
2 boxes for a medium order
3 boxes for a large order

The company has two different suppliers. Factory Q is 60 miles from the company Factory R is 180 miles from the company.

An experiment consists of monitoring a shipment and observing B, the number of boxes, and M, the number of miles the shipment travels. The following probabi ity model describes the experiment

Factory Q Factory R
small order 0.3 0.1
medium order 0.1 0.2
large order 0.2 0.1

(a) Find PB M(b, m), the joint PMF of the number of boxes and the distance