1. In your own words, differentiate deterministic from probabilistic processes:

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2. Differentiate random from stochastic processes:

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3. Differentiate the terms, "event" and "outcome."

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4. Define the terms, "event space" and "sample space," relating them to the concepts of event and outcome.

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5. Now, draw a Venn diagram, outlining in black the sample space for tossing a single die. On that diagram, use a red line to enclose the event space for those tosses that would turn up a prime number on the face of the die. Use a blue line to enclose the event space for those tosses turning up even numbers. Use a green line to mark the event space representing the intersection of the two event spaces.

6. Draw an outcome tree to show the probabilities of getting the following results from an I-Ching toss of three coins: HHH, HHT, HTH, THH, TTH, THT, HTT, and TTT:

For all problems (except # 12), do your calculations in Excel. Then, show all answers rounded to precisely 4 decimal places (e.g., 0.791145678 would be shown as 0.7911).

1. What is the probability of getting three coin tosses in a row, which all have the same side up?

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2. Which probability distribution is designed for such problems?

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3. What is the probability of getting exactly four heads in the course of eleven flips of an honest coin? Consult Eq. 5.2 in M&M:

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4. Let's say you have a dishonest coin, such that its probability of landing tail side up is 0.6. Now what would be the probability of getting exactly four heads in the course of eleven flips?

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5. Which probability distribution is appropriate for calculating the probability of getting a count of certain events within a given time period or within a given area and time period?

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6. On average, 2.5 camping groups turn up each day in the small Cucamonga Wilderness Area each summer. Consulting M&M Eq. 5.3, calculate the probability of getting no groups at all on a particular day next summer.

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7. Calculate the probability that the rangers will ahve to deal with anywhere between 1 and 3 (inclusive) parties of happy campers?

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8. Looking at the array of probabilities you calculated for X=0, 1, 2, and 3, which is the modal number of camping groups likely to descend on the area on any given summer day?

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9. Which probability distribution is appropriate for modeling the frequency of occurrence for a continuous variable, in which the distribution of cases is symmetrical and conforms to Tchebysheff's Theorem?

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10. Calculate the mean and the median for each of the following two sample data sets. Just using these two data descriptors, which of the two is likelier to have come from a normally distributed population? _____ A _____ B Why?

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    Sample A                   Sample B
                                      
        15.0                          1 
        21.2     mean (A)             4     mean (B)
        23.0                          5    
        19.1     _____                2     _____
        18.6                          6     
        17.3                          2   
        20.8     median (A)           5     median (B)
        16.7                          2
        18.9     _____                2     _____
        19.4                          7
                                      3
    --------------------------------------------------
    

11. Compute the standard deviations for each of these two data sets.
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    Sb = ____________________

12. Now, convert each distribution's scores into standard Z scores, using M&M Eq. 5.4. Round these answers to just 2 decimal places (since the Z table is shown to two places).

    
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    Sample A                   Sample B
    
        raw      Zi                  raw    Zi
                                      
        15.0     _____                1     _____
        21.2     _____                4     _____
        23.0     _____                5     _____
        19.1     _____                2     _____
        18.6     _____                6     _____
        17.3     _____                2     _____
        20.8     _____                5     _____
        16.7     _____                2     _____
        18.9     _____                2     _____
        19.4     _____                7     _____
                                      3     _____
    --------------------------------------------------
    

13. What is the probability that case 11 from Population A will exceed 20? Helpful hint for the bewildered: M&M, pp. 86-88 and Table A.

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14. What is the probability that case 12 from Population B will fall between 4.0 and 6.5?

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last revised: 09/22/98
© Dr. Christine M. Rodrigue