Questions: How many items are in this sample space? That is, how many possible outcomes did you find and list in part (a)? This value can be labeled as n(S) or S.

How many items are in this sample space? That is, how many possible outcomes did you find and list in part (a)? This value can be labeled as n(S) or S.

Transcript text: b. How many items are in this sample space? That is, how many possible outcomes did you find and list in part (a)? This value can be labeled as $\mathrm{n}(\mathrm{S})$ or $|\mathrm{S}|$.

Solution

Solution Steps

To determine the number of items in a sample space, we need to count the total number of possible outcomes. This can often be done by considering the different choices or events that can occur and multiplying the number of options for each event.

Step 1: Identify the Events

We have two events in our sample space. The first event has $ n_1 = 3 $ possible outcomes, and the second event has $ n_2 = 4 $ possible outcomes.

Step 2: Calculate the Total Outcomes

To find the total number of outcomes in the sample space $ n(S) $, we multiply the number of outcomes for each event: \[ n(S) = n_1 \times n_2 = 3 \times 4 = 12 \]