Question

the table below shows all of the possible outcomes for rolling two six - sided number cubes. table showing outcomes of two six - sided number cubes: rows for first number cube (1 - 6), columns for second number cube (1 - 6), cells with pairs like 1,1, 1,2,...6,6 how many possible outcomes are there? \bigcirc 6 \bigcirc 12 \bigcirc 21 \bigcirc 36

Explanation:

Step1: Analyze the table structure

The table represents the outcomes of rolling two six - sided number cubes. The first cube has 6 possible values (1 - 6) and for each value of the first cube, the second cube also has 6 possible values (1 - 6).

Step2: Calculate the total number of outcomes

We can calculate the total number of outcomes by multiplying the number of outcomes of the first cube by the number of outcomes of the second cube. The number of outcomes for the first cube \(n_1 = 6\) and for the second cube \(n_2=6\). Using the multiplication principle of counting, the total number of outcomes \(N=n_1\times n_2\).
Substitute \(n_1 = 6\) and \(n_2 = 6\) into the formula: \(N = 6\times6=36\). We can also count the number of cells in the table. The number of rows (corresponding to the first cube) is 6 and the number of columns (corresponding to the second cube) is 6. The total number of cells (outcomes) is \(6\times6 = 36\).

Answer:

36 (corresponding to the option "36")