Question

a spinner is separated into equal sections numbered 1 through 8. the spinner is spun, and two number cubes are rolled. how many possible outcomes contain all odd numbers?
12
20
36
288

Explanation:

Step1: Count odd - numbered sections on spinner

The spinner has 8 sections numbered 1 - 8. The odd - numbered sections are 1, 3, 5, 7. So there are 4 odd - numbered sections on the spinner.

Step2: Count odd numbers on a number cube

A number cube has 6 faces numbered 1 - 6. The odd numbers are 1, 3, 5. So there are 3 odd numbers on a number cube.

Step3: Use the counting principle for combined events

When two number cubes are rolled and a spinner is spun, the total number of outcomes with all odd numbers is the product of the number of odd - numbered outcomes for each event. The number of odd - numbered outcomes for the spinner is 4, and for each of the two number cubes is 3. So the total number of possible outcomes with all odd numbers is \(4\times3\times3=36\).

Answer:

36