1. An experimental crystallizer produces ?ve different polymorphs of the same crystal via mechanisms that are currently not well-understood. Types  1,  2  and  3 are approved for pharmaceutical application A; Types 2, 3 and 4 for a different application B; Type 5 is mostly unstable and has no known application. How much of each type is made in any batch varied randomly, but with the current operating procedure, 30% of the total product made by the crystallizer in a month is of Type 1; 20% is of Type 2, with the same percentage of Types 3 and 4; and 10% is of Type

2. Assuming  that  the polymorhps can  be  separated  without  loss,

(i) Determine the probability of making product in a month that can be used for application A;

(ii) Given a batch ready to be shipped for  application B, What is the probabilities that any crystal selected at random is of Type 2?  What  is  the probability  that  it  is of Type 3 or Type 4. State any assumptions you may need to make.

(iii) What is the probability that an order change to one for application A can be ?lled from a batch ready to be shipped for application B?

(iv) What is the converse probability that an order change to one for application B can be ?lled given a batch that is ready to be shipped for application A?