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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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