Math

QuestionList the sample space for choosing 2 marbles at random from a bag with green, red, and blue marbles.

Studdy Solution

STEP 1

Assumptions1. The bag contains more than one marble of each color green, red, and blue. . Two marbles are chosen at random from the bag.
3. The order of selection matters, meaning that picking a green marble first and a red marble second is different from picking a red marble first and a green marble second.

STEP 2

The sample space of an experiment is the set of all possible outcomes. In this case, the outcomes are the possible pairs of marbles that can be chosen.

STEP 3

We can list out all the possible outcomes by considering each color of marble for the first pick, and then each color of marble for the second pick.

STEP 4

If we pick a green marble first, the possible outcomes for the second pick are green, red, and blue. So the outcomes in this case are (Green, Green), (Green, Red), and (Green, Blue).

STEP 5

If we pick a red marble first, the possible outcomes for the second pick are green, red, and blue. So the outcomes in this case are (Red, Green), (Red, Red), and (Red, Blue).

STEP 6

If we pick a blue marble first, the possible outcomes for the second pick are green, red, and blue. So the outcomes in this case are (Blue, Green), (Blue, Red), and (Blue, Blue).

STEP 7

Combining all these outcomes, we get the sample space for this probability experiment.
The sample space is {(Green, Green), (Green, Red), (Green, Blue), (Red, Green), (Red, Red), (Red, Blue), (Blue, Green), (Blue, Red), (Blue, Blue)}.

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