Question

1. spinner a and spinner b have 3 color choices each: red, yellow and blue. what is the probability of getting a blue and yellow combination from the area model? event 1, spinner a: red, yellow, blue; event 2, spinner b: red, yellow, blue. options: 4/9, 2/9, 1/9, 1/3

Explanation:

Step1: Determine total outcomes

Spinner A has 3 colors, Spinner B has 3 colors. Total outcomes from area model (grid) is \(3\times3 = 9\) (since it's a \(3\times3\) grid).

Step2: Identify favorable outcomes

We need blue (from Spinner A) and yellow (from Spinner B), or yellow (from Spinner A) and blue (from Spinner B)? Wait, the problem says "blue and yellow combination". Let's check the grid: Spinner A rows (Red, Yellow, Blue) and Spinner B columns (Red, Yellow, Blue). So the cells are (A color, B color). So blue from A (row Blue) and yellow from B (column Yellow) is 1 cell. Also, yellow from A (row Yellow) and blue from B (column Blue) is another? Wait no, wait the problem says "blue and yellow combination" – maybe order? Wait the area model: let's see the grid. Rows: Spinner A (Red, Yellow, Blue), Columns: Spinner B (Red, Yellow, Blue). So each cell is (A, B). So "blue and yellow" could be (Blue, Yellow) or (Yellow, Blue)? Wait no, the problem says "getting a blue and yellow combination" – maybe the two spinners, so one is blue and the other is yellow. Let's count the number of such cells. Spinner A Blue (row) and Spinner B Yellow (column): 1 cell. Spinner A Yellow (row) and Spinner B Blue (column): 1 cell. Wait, but maybe the problem considers "blue and yellow" as any order? Wait no, maybe the problem is (Spinner A, Spinner B) as (blue, yellow) or (yellow, blue)? Wait let's re-examine. Wait the grid is 3x3=9 cells. Let's list all cells:

(Red, Red), (Red, Yellow), (Red, Blue),

(Yellow, Red), (Yellow, Yellow), (Yellow, Blue),

(Blue, Red), (Blue, Yellow), (Blue, Blue).

So the combinations where one is blue and the other is yellow: (Blue, Yellow) and (Yellow, Blue). So that's 2 cells? Wait but the options include 2/9. Wait the options are 4/9, 2/9, 1/9, 1/3. Wait maybe I misread. Wait the problem says "getting a blue and yellow combination" – maybe the problem is (Spinner A is blue and Spinner B is yellow) or (Spinner A is yellow and Spinner B is blue)? Wait no, maybe the problem is "blue and yellow" regardless of order, but let's check the grid again. Wait the user's image: the grid has Spinner A (Event 1) with rows Red, Yellow, Blue (vertical), and Spinner B (Event 2) with columns Red, Yellow, Blue (horizontal). So each cell is (A, B). So "blue and yellow" – let's see the problem statement: "What is the probability of getting a blue and yellow combination from the area model?" So how many cells have one blue and one yellow? Let's count:

• (Blue, Yellow): 1 cell (row Blue, column Yellow)

• (Yellow, Blue): 1 cell (row Yellow, column Blue)

So total favorable outcomes: 2. Total possible outcomes: 9. So probability is 2/9? Wait but let's check the options. 2/9 is an option. Wait but maybe I made a mistake. Wait maybe the problem is (Spinner A is blue and Spinner B is yellow) only? Let's check the grid: row Blue (Spinner A) and column Yellow (Spinner B) is 1 cell. Then row Yellow (Spinner A) and column Blue (Spinner B) is another. So 2 cells. So 2/9. Wait but let's confirm. Total outcomes: 3x3=9. Favorable: 2 (Blue-Yellow and Yellow-Blue). So probability is 2/9.

Step3: Calculate probability

Probability = (Number of favorable outcomes) / (Total number of outcomes) = 2/9.

Answer:

\(\frac{2}{9}\) (Option: \(\frac{2}{9}\))