If I have a bag filed with 6 marbles, 2 blue marbles, and 4 yellow marbles, and I had to pick one from the bag, what is my sample space?
To determine the sample space of an experiment, we need to identify all the possible outcomes. In this case, the experiment is picking one marble from the bag.
The sample space, denoted by S, is the set of all possible outcomes. Since there are 6 marbles in total (2 blue and 4 yellow), the sample space can be represented as:
S = {blue, blue, yellow, yellow, yellow, yellow}
Here, each element of the set represents one possible outcome of picking a marble from the bag. The first two elements represent the blue marbles, and the remaining four elements represent the yellow marbles.
To determine the sample space, we need to list all the possible outcomes of picking one marble from the bag. In this case, the possible outcomes are the different types of marbles that can be selected.
The two types of marbles in the bag are blue and yellow. So, the sample space is:
Sample Space: {blue marble, yellow marble}
Therefore, the sample space for picking one marble from the bag is {blue marble, yellow marble}.