Question

• lin creates a tree to keep track of the outcomes.

1. how many outcomes are in the sample space for this experiment?
2. one of the outcomes from diegos list is blx. where does this show up in tylers method? where is it in lins method?
3. when spinning all three spinners, what is the probability that:

a. they point to the letters any? explain your reasoning.
b. they point to the letters amw, anz, or bnw? explain your reasoning.

1. if a fourth spinner that has 2 equal sections labeled s and t is added, how would each of the methods need to adjust?

Explanation:

Step1: Count outcomes per branch

First level: 3 nodes (A/B, L/M/N). Second level: 4 nodes each.
Total outcomes: $3 \times 4 = 12$ per tree, but combined sample space is $3 \times 4 = 12$? No, wait: Each first node (A/B) has 3 second nodes, each with 4 outcomes. So total: $2 \times 3 \times 4 = 24$

Step2: Verify total outcomes

Each main branch (A, B) has 3 sub-branches (L/M/N), each with 4 final outcomes. $2 \times 3 \times 4 = 24$

Diego's list (BLX) would be a combined label of the three spinners: first spinner lands on B, second on L, third on X. In Lin's tree method, this is the path starting at B, then moving to the L branch, and finally to the X endpoint on that L branch.

Part a:

Step1: Calculate total outcomes

Total sample space size: $2 \times 3 \times 4 = 24$

Step2: Count favorable outcomes

ANY is one specific combination. Number of favorable outcomes = 1

Step3: Compute probability

Probability = $\frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{1}{24}$

Part b:

Step1: Count favorable outcomes

AMW, ANZ, BNW are 3 distinct specific combinations. Favorable outcomes = 3

Step2: Compute probability

Probability = $\frac{3}{24} = \frac{1}{8}$

For Tyler's list method: Every existing outcome label would be extended by adding either S or T at the end, doubling the total number of listed outcomes. For Lin's tree method: Each final endpoint (W/X/Y/Z) on the existing tree would have two new branches extending from it, labeled S and T, which doubles the total number of endpoints in the tree.

Answer:

24

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