1. Tom rolled an ordinary pair of six-sided dice 50 times. After each roll of the dice Tom calculated the sum of the two numbers and recorded the sum frequencies in the table shown. Use this information to answer the following questions:

Sum 2 3 4 5 6 7 8 9 10 11 12

Frequency 2 3 5 5 6 8 7 5 4 3 2

(a)What fraction, or part, of the 50 rolls resulted in a sum less than 6? (Express your answer in decimal form.)

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(b)Theoretically, what is the probability that the sum of the dice will be less than 6? (Express your answer in decimal form.)

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2. Mary's final exam scores for 1992-1996 are indicated in the graph. Use this graph to answer the following questions:

(a) Mary took exams in 1997 and 1998. Her mean score for the years 1992-1998 was 82. What was the sum of Mary's scores for 1997 and 1998?

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(b) List two possible final exam scores for 1997 and 1998 that would give Mary a median score of 83 for the years 1992-1998.

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3. A student reaches three times into a fruit basket containing 4 apples, 4 oranges, and 4 bananas to get 3 pieces of fruit.

(a) How many different collections (or combinations) of 3 pieces of fruit could the student get?

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(b) What is the probability that the student will get 3 of the same fruit? (Express your answer in fraction form.)

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4. (a) A company is creating new employee identification codes for its employees. Each employee's identification code will be made of 1 capital letter followed by 2 single-digit numbers (such as Q13). The letters O and I will not be used in these codes. How many different employee codes are available to this company?

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(b) How many employee codes would be available to the company if the two-digit number of the code could not contain the same two digits?

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5. In a collection of 80 books, 34 have leather covers and 18 were published before 1900. If 42 of these books were published after 1900 and do not have leather covers, how many books were published before 1900 and have leather covers?

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