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					                              ES 85
                          Bonus Problems

  NOTE: Only for the students who incurred a raw score of at most 99.
  This is just to obtain the 60% prelim grade.

1. Students at College of Engineering (MSU-IIT) are classified according
   to regular year level, and also according to whether they are male or
   female. Find the total number of possible classifications.
2. How many different letter arrangements can be made from the letters
   in the word of STATISTICS?
3. In a certain region of the country it is known from (last, experience
   that the: probability of selecting an adult over 40 years of age: with
   cancer is 0.05, If the probability of a doctor correctly diagnosing a
   person with cancer as having the disease is 0.78 and the probability
   of incorrectly diagnosing a person without cancer as having the
   disease is 0.06. Draw the tree diagram.
   (a) What is the probability that a person is diagnosed as having
       cancer?
   (b) What is the probability that a person diagnosed as having cancer
   actually has the disease?
4. (a) In how many ways can 6 people be lined up to get on a bus?
   (b) If 3 specific persons, among 6, insist on following each other, how
   many ways are possible?
   (c) If 2 specific persons, among 6, refuse to follow each other, how
   many ways are possible?
5. How many ways are there that no two students will have the same
   birth date in a size of 60 class?

				
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