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The possible outcomes. The top row indicates the numbers on the sides of the blue die and the first column represents the number on the sides of the red die. The white area indicates the sum of the numbers in the row and column.

\begin{tabular}{|c|c|c|c|c|c|c|}
\hline
\# Rolled & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline
1 & 2 & 3 & 4 & 5 & 6 & 7 \\ \hline
2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline
3 & 4 & 5 & 6 & 7 & 8 & 9 \\ \hline
4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline
5 & 6 & 7 & 8 & 9 & 10 & 11 \\ \hline
6 & 7 & 8 & 9 & 10 & 11 & 12 \\ \hline
\end{tabular}

How many outcomes are in the sample space?

(Note: [tex]$3+2=5$[/tex] (3 on red die and 2 on blue die) is not the same as [tex]$2+3=5$[/tex] (2 on red die and 3 on blue die)).



Answer :

GinnyAnswer
When determining the total number of outcomes in the sample space, you need to consider every possible result that can occur from rolling each die. Here’s how you can think about it step by step:

1. Identify the number of sides on each die:
- The red die has 3 sides.
- The blue die has 2 sides.

2. Determine the total number of possible outcomes:
- Each side of the red die can pair with each side of the blue die.
- To find the total number of outcomes, you multiply the number of sides on the red die by the number of sides on the blue die.

Mathematically, this method can be described as:
[tex]\[ \text{Number of outcomes} = (\text{Number of sides on red die}) \times (\text{Number of sides on blue die}) \][/tex]

Plugging in the values:
[tex]\[ \text{Number of outcomes} = 3 \times 2 = 6 \][/tex]

So, the total number of outcomes in the sample space is 6.

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