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1. Suppose that a sample space S consists of four simple events: A, B, C, and D. That is S = {A, B, C, D}. If P(A) = .4, P(B) = .3, P(C) = .2, what is P(D)?

   1.   ?    .1
   2.   ?    .9
   3.   ?    .024
   4.   ?    None of the answers given; click to see the solution.

2. A box contains four equally-sized tickets, numbered 1, 2, 3 and 4, and a second box contains three tickets also of the same size, numbered 4, 5, and 6. An experiment consists of selecting one ticket from the first box and then selecting one ticket from the second box. Write the sample space for this experiment. Note: This problem will be continued in questions 3 and 4.

   1.   ?    {(1,4), (1,5), (1,6) (2,4), (2,5), (2,6), (3,4), (3,5), (3,6), (4,4), (4,5), (4,6)}
   2.   ?    {1, 2, 3, 4, 5, 6}
   3.   ?    12
   4.   ?    None of the answers given; click to see the solution.

3. Using the same experiment and sample space as in question #2, what is the probability that tickets with the same numbers are chosen from each box?

   1.   ?    1/12
   2.   ?    1
   3.   ?    1/3
   4.   ?    None of the answers given; click to see the solution.

4. Using the same experiment and sample space as in question #2, what is the probability that the sum of the numbers on the tickets chosen is at least 7?

   1.   ?    3/4
   2.   ?    9
   3.   ?    1/4
   4.   ?    None of the answers given; click to see the solution.

5. An experiment consists of dealing 7 cards from a standard 52-card deck. What is the probability of being dealt 5 hearts and 2 spades?

   1.   ?    .00075
   2.   ?    100,386
   3.   ?    .0000102
   4.   ?    

6. An organization has 40 members, of whom 25 are females and 15 are males. If a President and Vice-President are chosen at random, what is the probability that both are females?

   1.   ?    .38
   2.   ?    600
   3.   ?    5/8
   4.   ?    None of the answers given; click to see the solution.

7. Suppose there are 6 people in a room. Each person writes his or her name on a piece of paper. The papers are collected, mixed together, and then one paper is returned to each person. What is the probability that each person gets the paper with his or her name back?

   1.   ?    1/6! = .00139
   2.   ?    1/6
   3.   ?    720
   4.   ?    None of the answers given; click to see the solution.