Questions: An experiment is performed where a 4-sided die is rolled and then another 4-sided die is rolled. The possible outcomes for both events are 1,2,3 and it identify the sample space for this experiment.

Solution Steps

To identify the sample space for the experiment where two 4-sided dice are rolled, we need to list all possible outcomes. Each die can land on any of the four faces (1, 2, 3, or 4), so we will have a combination of these outcomes for the two dice.

When rolling two 4-sided dice, each die can land on one of the four faces: \(1, 2, 3, 4\). Therefore, the total number of outcomes for the two dice can be represented as the Cartesian product of the outcomes of each die.

The sample space \(S\) for this experiment consists of all possible ordered pairs \((i, j)\) where \(i\) is the outcome of the first die and \(j\) is the outcome of the second die. The complete sample space is given by: \[ S = \{(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4), (4, 1), (4, 2), (4, 3), (4, 4)\} \]

The total number of outcomes in the sample space can be calculated as: \[ \text{Total Outcomes} = 4 \times 4 = 16 \]

Final Answer