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 Spinner A.

Step2: Analyze Spinner B outcomes

Spinner B has 4 numbers (1, 2, 3, 4). Spinning it once gives 4 possible outcomes.

Step3: Calculate total outcomes

By the multiplication principle, the total number of possible outcomes when spinning Spinner A twice and Spinner B once is 9×4=36. We need to find the tree - diagram that represents 36 outcomes.

Answer:

We need to count the number of end - points in each tree - diagram option. Without seeing the full details of each option, we know the correct tree - diagram should have 36 end - points. If we assume the structure of the tree - diagrams follows the correct logic of first branching for Spinner A's two spins and then for Spinner B's spin, we can analyze the complexity of the diagrams. Since we have 3 initial branches for the first spin of Spinner A, each of those branches has 3 sub - branches for the second spin of Spinner A, and then each of those resulting branches has 4 final branches for Spinner B. A complete tree - diagram with the correct number of branches and end - points will be the answer. If we assume the diagrams are drawn correctly in terms of the spinning order, the diagram with the most complex branching structure (corresponding to 3×3×4 = 36 outcomes) is the correct one. However, since the actual visual details of the diagrams are not fully clear in text form, if we had to guess based on the principle of counting outcomes, we look for a diagram that has a large number of end - points consistent with our calculation. If we assume the diagrams are labeled and structured as described, we need to find the one that shows all the possible combinations. Without seeing the full visual details of each option, we can't definitively point to a lettered choice, but the correct diagram should show 36 distinct end - states.