Question

a hat contains 4 marbles; one blue, one green, one orange, and one red. 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 □ sample points in the sample space.

Explanation:

Step1: Analyze the first selection

There are 4 marbles for the first selection.

Step2: Analyze the second selection

After the first marble is selected (without replacement), there are 3 marbles left for the second selection.

Step3: Apply the fundamental counting principle

The total number of ways to select two marbles is the product of the number of ways for each selection. Using the formula \(n = m_1\times m_2\), where \(m_1 = 4\) (first - selection) and \(m_2=3\) (second - selection). So \(n=4\times3\).

Answer:

12