Question

one spinner has two sections. they are marked a and b. another spinner has five sections. they are marked 1, 2, 3, 4, and 5. the two spinners are spun. the tree diagram below shows the possible outcomes. use the diagram to answer the questions. first spinner second spinner outcome 1 (a,1) 2 (a,2) 3 (a,3) 4 (a,4) 5 (a,5) 1 (b,1) 2 (b,2) 3 (b,3) 4 (b,4) 5 (b,5) (a) how many outcomes are there? \square outcome(s) (b) how many outcomes involve landing on 2 or 3? \square outcome(s) (c) how many outcomes involve landing on b and an even number? \square outcome(s)

Explanation:

Part (a)

Step1: Count outcomes for A

First spinner on A: 5 outcomes (A,1) to (A,5).

Step2: Count outcomes for B

First spinner on B: 5 outcomes (B,1) to (B,5).

Step3: Total outcomes

Add outcomes for A and B: $5 + 5 = 10$.

Step1: Outcomes with 2 or 3 for A

For A: (A,2), (A,3) → 2 outcomes.

Step2: Outcomes with 2 or 3 for B

For B: (B,2), (B,3) → 2 outcomes.

Step3: Total outcomes

Add outcomes for A and B: $2 + 2 = 4$.

Step1: Identify even numbers

Even numbers in second spinner: 2, 4.

Step2: Outcomes with B and even

For B: (B,2), (B,4) → 2 outcomes.

Answer:

10

Part (b)