Question: Problem 2.3

Acme has specially made containers they use for shipping; each container contains 48 tires of the same type. Thus, a container will either hold exactly 48 all weather tires or 48 high performance tires. Due to a bug in the factory computer system, all the tires currently in the warehouse are unlabeled, so it is impossible to differentiate between containers of each type of tire. (for simplicity, assume that there are an infinite number of containers in the warehouse). You do know that 72% of the tires in the warehouse are all weather tires and 28% are high performance tires. Suppose a retailer places an order for 4 containters of all weather tires.

(a) If you pull four containers chosen at random from the warehouse, what is the probability that all four contain all weather tires?
(b) If you pull seven containers chosen at random from the warehouse, what is the probability that you will pull exactly four that contain all weather tires?
(c) If you pull seven containers chosen at random from the warehouse, what is the probability that you will pull at least four that contain all weather tires?