The problem involves drawing two balls from an urn containing 15 numbered balls (numbered 1 through 15), without replacement. Let's break this down:

1. Size of the Sample Space:

The sample space refers to all possible outcomes of drawing two balls, noting their numbers, and considering that the order matters (since the numbers of both balls are recorded).

• For the first draw, there are 15 possible outcomes (since the urn has 15 balls).
• After the first ball is drawn and not replaced, there are 14 remaining balls for the second draw.

Thus, the total number of possible outcomes (the size of the sample space) is the product of the possible outcomes of both draws: $\text{Size of Sample Space} = 15 \times 14 = 210$

2. Example of an Outcome:

An example of an outcome is drawing ball number 7 on the first draw and ball number 12 on the second draw. We can represent this outcome as: $(7, 12)$

Here, the order is important because drawing ball 7 first and ball 12 second is a different outcome from drawing ball 12 first and ball 7 second.

Summary:

• Size of the Sample Space: 210
• Example of an Outcome: (7, 12)

Would you like further details on sample space, or have any questions?

Here are 5 related questions you might find helpful:

1. How does the sample space change if the balls were replaced after each draw?
2. What if the order of the balls did not matter in this experiment? How would the sample space size change?
3. How many possible outcomes would there be if three balls were drawn instead of two, without replacement?
4. How would the sample space change if the urn contained 20 balls instead of 15?
5. What if we only cared about the sum of the two balls' numbers? How would the experiment change?

Tip: When calculating the size of the sample space for problems involving drawing items without replacement, always reduce the number of available items with each subsequent draw!