Question 5, 11.4.13 HW Score: $$ 40 \%, 4 $$ of 10 points Part 1 of 6 Points: 0 of 1 Save A hat contains 4 marbles; one yellow, one red, one green, and one blue. Two marbles are selected at random without replacement from the hat. Complete parts a) through e). Use the fundamental counting principle to determine the answer to part a). Assume that each event is equally likely to occur. a) Determine the number of sample points in the sample space. There are $$ \square $$ sample points in the sample space.

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**Step 1. Determine the number of ways to pick the first marble.**

Since there are 4 marbles, there are  
$$
4
$$  
ways to choose the first marble.

**Step 2. Determine the number of ways to pick the second marble.**

Once the first marble is chosen, there are 3 remaining marbles. Thus, there are  
$$
3
$$  
ways to choose the second marble.

**Step 3. Apply the Fundamental Counting Principle.**

The Fundamental Counting Principle tells us that if one event can occur in $$ n $$ ways and a second event can occur in $$ m $$ ways, then the two events together can occur in  
$$
n \times m
$$  
ways.

Here, the total number of sample points is:  
$$
4 \times 3 = 12.
$$

**Final Answer:**

There are $$ 12 $$ sample points in the sample space.
There are 12 sample points in the sample space.

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