Math 3118, section 1

Fall 2002

Review questions for the first test

Click here to see solutions to some of these problems.

1. ( Not covered on the test, but work as many as you find helpful as background for the Chapter 7 material; these problems are also mentioned in another posting on the class homepage. )
   • Sec. 2.2 # 1, 2, 3, 5, 6, 8, 11
   • Sec. 2.3 # 4, 5, 9, 26, 27, 31, 32, 33, 34
   • Sec. 2.5 # 5, 6, (and subsequent exercises corresponding to the parts of exercise 7.1.10 that you work)
      
2. Two exercises from the text:
   • Exercise 7.1.10
   • Exercise 7.3.9
      
3. Two more exercises from the text:
   • Exercise 7.6.7
   • Exercise 7.6.8
      
   Useful background info: The number of distinct words ( ¡ including nonsense words ! )
   that can be formed from the letters of the word READER is:
               = 15·6·2 = 180.
   • First factor: choose 2 spots for the two E's
   • Second factor: choose 2 of the 4 remaining spots for the two R's
   • Third factor: arrange the remaining letters (A and D) in either order.
   For further details, see section 3 of chapter 2, (or your own notes from Math 3113).
    
   In working exercise 7.6.7, you'll need to count the number of words in which the two E's are adjacent;   in working exercise 7.6.8, you'll need to count the number of entities of a slightly different (but similar) nature ...
    
4. Two miscellaneous exercises
   1. This exercise refers to Table 7.2, in section 7.5 of the text.
      1. A student is chosen at random from among the 25, and that student's eyes are not blue [and thus brown, green, or hazel ... ]. What is the probability that the student is female?   In other words, what is the probability that the student is female, given that the student's eye color is not blue?
          
      2. A student is chosen at random from among the 25, and that student is female. What is the probability that the student's eyes are not blue? In other words, what is the probability that the student's eyes are not blue, given that the student is female.
          
      • Suggestion: If you wish, you may refer to the diagrams on pages 152 and 153 of the text.
         
      • Comment: You may get different answers on the two parts. In general,  p(E|F) need not be the same as p(F|E).
         
   2. Three cards are drawn at random from a standard deck of 52 cards.
      1. What is the probability that all 3 cards are diamonds?
          
      2. What is the probability that all 3 cards are red?
          
      3. What is the probability that all 3 cards are face cards?
         In other words, what is the probability that a king, a queen, and a jack were drawn?
          
      4. What is the probability that the 3 cards are the king of diamonds, the queen of diamonds, and the jack of diamonds?
          
      5. What is the (conditional) probability that all 3 cards are diamonds, given that all 3 cards are red?
          
      6. What is the (conditional) probability that all 3 cards are face cards, given that all 3 cards are diamonds?
          
      7. What is the (conditional) probability that the 3 cards are the king of diamonds, the queen of diamonds, and the jack of diamonds, given that all 3 cards are face cards?
      
       
   3. Review the exercises that were done as group work and homework assignments

       

   Solutions are now linked here.  

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