Question

homework: unit 4 - mean, median and mode, and probability
question 25, 7.4.7
part 1 of 2
draw a tree - diagram for spinning spinner a two times and then spinner b one time. use the diagram to find the number of possible outcomes.

Explanation:

Step1: Analyze Spinner A outcomes

Spinner A has 3 colors (Red - R, Blue - B, Yellow - Y). Spinning it twice gives 3×3 = 9 possible pairs of outcomes for the two - spins of Spinner A: (R,R), (R,B), (R,Y), (B,R), (B,B), (B,Y), (Y,R), (Y,B), (Y,Y).

Step2: Analyze Spinner B outcomes

Spinner B has 4 equal sections numbered 1 - 4. For each of the 9 pairs of outcomes of Spinner A, there are 4 possible outcomes from Spinner B.

Step3: Calculate total outcomes

By the multiplication principle, the total number of possible outcomes is 9×4=36.

Answer:

We need to draw a tree - diagram that first branches out for the two spins of Spinner A (with 3 branches at each of the two levels for Spinner A's spins) and then for each of the resulting branches, we have 4 branches for Spinner B's outcomes. Without seeing the exact details of the tree - diagrams in options A, B, C, D, we know the correct tree - diagram should represent 36 possible outcomes. If we assume the tree - diagrams are drawn correctly in terms of structure for the spinners' spins, we can eliminate diagrams that don't have the correct number of end - points (leaves) corresponding to 36 outcomes. But since we are not asked to choose from the diagrams but rather understand the process, the key is to know the total number of outcomes is 36 and the tree - diagram should be structured to show the two spins of Spinner A first and then the spin of Spinner B for each combination of Spinner A's spins.