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) how many outcomes are there? (b) how many outcomes involve landing on 1 or 2? (c) how many outcomes involve landing on a and an odd number?

Explanation:

Step1: Calculate total number of outcomes

Use multiplication principle. First spinner has 2 options, second has 3, and third has 2. So total is $2\times3\times2$.
$2\times3\times2 = 12$

Step2: Count outcomes with 1 or 2 on second - spinner

For each of the 2 outcomes of the first spinner and 2 outcomes of the third spinner, when the second - spinner lands on 1 or 2 (2 options), the number of outcomes is $2\times2\times2$.
$2\times2\times2=8$

Step3: Count outcomes with A and odd number on second - spinner

Odd numbers on second spinner are 1 and 3. For first spinner outcome A, and for each of the 2 outcomes of the third spinner and 2 odd - number outcomes of the second spinner, the number of outcomes is $1\times2\times2$.
$1\times2\times2 = 4$

Answer:

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