1. Based on past experience, a company knows that an experienced machine operator will pro- duce a defective item 2% of the time. Operators with some experience produce a defective item 3.5% of the time, and new operators will produce a defective item 9% of the time. At any one time, the company has 53% experienced operators, 33% operators with some experience, and 14% new operators. (a) Draw a tree diagram using the given information. (b) Given that an item is defective, what is the probability that it was made by a new operator