Question

one spinner has two sections. they are marked a and b. another spinner has three sections. they are marked 1, 2, and 3. a third spinner has two sections. one is green and one is pink. the three spinners are spun. the tree diagram below shows the possible outcomes. use the diagram to answer the questions. first spinner second spinner third spinner outcome (a, 1, green) (a, 1, pink) (a, 2, green) (a, 2, pink) (a, 3, green) (a, 3, pink) (b, 1, green) (b, 1, pink) (b, 2, green) (b, 2, pink) (b, 3, green) (b, 3, pink) (a) how many outcomes are there? outcome(s) (b) how many outcomes involve landing on 1 or 2? outcome(s) (c) how many outcomes involve landing on b and an odd number? outcome(s)

Explanation:

Step1: Calculate total outcomes

For the first spinner (2 options), second spinner (3 options), third spinner (2 options). Use the multiplication principle: \(2\times3\times2\).

$$2\times3\times2 = 12$$

Step2: Calculate outcomes for landing on 1 or 2 (second - spinner)

First spinner has 2 options, second spinner (1 or 2, 2 options), third spinner has 2 options. \(2\times2\times2\)

$$2\times2\times2=8$$

Step3: Calculate outcomes for landing on B (first - spinner) and odd number (second - spinner: 1 or 3)

First spinner (1 option: B), second spinner (2 odd - number options: 1,3), third spinner (2 options). \(1\times2\times2\)

$$1\times2\times2 = 4$$

Answer:

a. \(12\)
b. \(8\)
c. \(4\)