Question

use the spinner shown to answer the question. assume that it is equally probable that the pointer will land on any one of the colored regions. if the pointer lands on a borderline, spin again. if the spinner is spun once, find the probability that the pointer lands in a region that is green or yellow. the probability that the pointer lands in a region that is green or yellow is \\(\square\\) (type an integer or a simplified fraction.)

Explanation:

Step1: Count total regions

The spinner has 8 equal regions (from the diagram: 2 green, 2 yellow, 2 red, 2 blue? Wait, looking at the spinner: green regions: 2, yellow regions: 2, red: 2, blue: 2? Wait no, let's count again. The spinner is divided into 8 parts. Let's list the colors: green, yellow, blue, red, red, green, yellow, blue? Wait no, the diagram shows: top yellow, blue, red, green; bottom red, green, yellow, blue? Wait no, looking at the spinner: let's count the number of green and yellow regions. Green regions: 2 (one on top right, one on bottom middle). Yellow regions: 2 (top left, bottom right). Total regions: 8. So number of green or yellow regions: 2 (green) + 2 (yellow) = 4. Wait, no: wait the spinner: let's see the colors: yellow, blue, red, green (top half), then red, green, yellow, blue (bottom half)? Wait no, the spinner is divided into 8 equal sectors. Let's count green: 2 (yes, two green sectors), yellow: 2 (two yellow sectors). So total favorable (green or yellow) is 2 + 2 = 4. Total possible: 8. So probability is number of favorable / total = 4/8 = 1/2? Wait no, wait maybe I miscounted. Wait the spinner: let's look again. The user's spinner: colors are yellow, blue, red, green (top row), then red, green, yellow, blue (bottom row)? Wait no, the diagram: top: yellow, blue, red, green; bottom: red, green, yellow, blue? Wait no, the spinner has 8 sectors. Let's count green: 2 (one at 3 o'clock, one at 6 o'clock? No, looking at the image: the spinner has: yellow (top left), blue (top right), red (middle right), green (middle right? No, wait the spinner is a circle divided into 8 equal parts. Let's count the number of green regions: 2 (yes, two green sectors), yellow regions: 2 (two yellow sectors). So total green or yellow: 2 + 2 = 4. Total sectors: 8. So probability is 4/8 = 1/2? Wait no, wait maybe I made a mistake. Wait let's count again. The spinner: let's list each sector:

1. Yellow (top left)
2. Blue (top middle)
3. Red (top right)
4. Green (middle right)
5. Red (bottom right)
6. Green (bottom middle)
7. Yellow (bottom left)
8. Blue (bottom middle left)

Wait no, that's not right. Wait the spinner is divided into 8 equal parts. Let's count green: sectors 4 and 6: 2. Yellow: sectors 1 and 7: 2. So green or yellow: 2 + 2 = 4. Total sectors: 8. So probability is 4/8 = 1/2. Wait but maybe I miscounted. Wait the problem says "green or yellow". So number of green regions: 2, yellow regions: 2. So total favorable: 2 + 2 = 4. Total possible: 8. So probability is 4/8 = 1/2.

Step2: Calculate probability

Probability = (Number of green regions + Number of yellow regions) / Total number of regions.

Number of green regions = 2, Number of yellow regions = 2, Total regions = 8.

So Probability = (2 + 2) / 8 = 4/8 = 1/2.

Answer:

$\frac{1}{2}$