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<b>Deterministic Probability - The Marble Game Example</b>

<b>Use the information in the following setting to answer questions 1 through 7:</b>

While in Romania last year I noticed a group of children playing a game with a set of marbles.
The rules seemed a bit complicated (especially because I did not speak the local language) but
the game pieces were interesting enough to motivate this example. There were 20 marbles in
the set. Six of the colors - red, blue, purple, orange, green, and brown - came in three patterns.
The possible patterns were solid, striped, and speckled; so there was one solid red, one striped
red and one speckled red... etc. In addition, there was a single speckled grey marble as well as
a solid black one. Consider that all of these marbles were placed into a bag and one was
selected at random. Of interest is the color and/or pattern of the selected marble. Note that
this sampling scheme is called a Simple Random Sampling design (SRS) …but more on that
later.

1) Briefly describe the sample space (list all outcomes):

3) Find the probabilities of the following events:
A) P(red) =

B) P(red and speckled) =

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D) P(purple or blue) =

E) P(grey speckled) =

F) P(grey solid) =

G) P(black or striped) =

H) P( orange or solid) =

I) P(green | striped) =

J) P(striped | green) =

K) P(solid | black) =

4) From within the results of parts 3A through 3K identify any “impossible” events

5) From within the results of parts 3A through 3K identify any “certain” events

6) Support or oppose the following and defend your choice in one or two sentences and
appropriate calculations: “Color and pattern are independent” (extra credit)

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