Question

assume that the spinner to the right cannot land on a line. assume all sectors of the spinner are the same size. complete parts (a) through (c) below.
(a) give the probability that the spinner shown would land on red.
the probability is
(type an integer or a simplified fraction.)
(b) give the probability that the spinner shown would land on yellow.
the probability is
(type an integer or a simplified fraction.)
(c) give the probability that the spinner shown would land on blue.
the probability is
(type an integer or a simplified fraction.)

Explanation:

Step1: Count total sectors

The spinner has 5 sectors? Wait, no, looking at the colors: Red, Yellow, Red, Yellow, Blue. Wait, no, let's count again. The spinner: Red (1), Yellow (1), Red (2), Yellow (2), Blue (1). Wait, no, the diagram: let's see the sectors. From the image, the spinner is divided into 5? Wait, no, maybe I miscounted. Wait, the colors: Blue (1), Red (1), Yellow (1), Red (2), Yellow (2). Wait, no, let's check the number of each color. Red: 2 sectors? Wait, no, the image: Blue is 1, Red is 2, Yellow is 2? Wait, no, looking at the pie chart: Blue (1), Red (1), Yellow (1), Red (2), Yellow (2)? Wait, no, maybe it's 5 sectors? Wait, no, the problem says "all sectors of the spinner are the same size". Wait, let's count the number of red, yellow, blue. Red: 2 sectors, Yellow: 2 sectors, Blue: 1 sector? Wait, no, that can't be. Wait, maybe I made a mistake. Wait, the pie chart: let's see the angles. Wait, the spinner has 5 equal sectors? No, wait, the colors: Blue (1), Red (1), Yellow (1), Red (2), Yellow (2). Wait, no, maybe it's 5 sectors? Wait, no, the total number of sectors: let's count the regions. Blue: 1, Red: 2, Yellow: 2. Wait, 1+2+2=5? No, 1+2+2=5? Wait, no, 1 (blue) + 2 (red) + 2 (yellow) = 5? Wait, but the problem says "all sectors of the spinner are the same size". Wait, maybe each sector is equal, so total number of sectors: let's see, the spinner has 5 sectors? Wait, no, looking at the diagram, the blue is one sector, red is two sectors, yellow is two sectors? Wait, no, maybe I miscounted. Wait, the correct way: probability is (number of red sectors) / (total number of sectors). Let's look at the image again. The spinner: Blue (1), Red (1), Yellow (1), Red (2), Yellow (2). Wait, no, maybe it's 5 sectors? Wait, no, the problem says "all sectors of the spinner are the same size". So total number of sectors: let's count the number of regions. Blue: 1, Red: 2, Yellow: 2. Wait, 1+2+2=5? No, 1+2+2=5? Wait, no, 1 (blue) + 2 (red) + 2 (yellow) = 5? Wait, but 1+2+2=5? Wait, no, 1+2+2=5? Wait, maybe it's 5 sectors. Wait, no, maybe I made a mistake. Wait, the correct count: looking at the pie chart, the sectors are: Blue (1), Red (1), Yellow (1), Red (2), Yellow (2). Wait, no, maybe it's 5 sectors? Wait, no, the problem says "all sectors of the spinner are the same size", so each sector has equal area. So let's count the number of red sectors: 2, yellow: 2, blue: 1? Wait, no, that would be 5 sectors. Wait, but 2+2+1=5. So total sectors: 5? Wait, no, maybe I miscounted. Wait, the image: let's see, the spinner is divided into 5 equal parts? No, maybe 5? Wait, no, the colors: Blue (1), Red (1), Yellow (1), Red (2), Yellow (2). Wait, no, maybe it's 5 sectors. So for part (a), probability of red: number of red sectors / total sectors. Red sectors: 2, total sectors: 5? Wait, no, wait, maybe I made a mistake. Wait, the problem says "all sectors of the spinner are the same size". Let's look at the diagram again. The spinner: Blue (1), Red (1), Yellow (1), Red (2), Yellow (2). Wait, no, maybe it's 5 sectors. So red: 2, yellow: 2, blue: 1. Wait, but 2+2+1=5. So total sectors: 5. So probability of red: 2/5? Wait, no, wait, maybe I miscounted. Wait, the correct way: let's count the number of each color. Red: 2 sectors, Yellow: 2 sectors, Blue: 1 sector. Total sectors: 2+2+1=5. So for (a), probability of red is 2/5? Wait, no, wait, maybe the spinner has 5 sectors? Wait, no, maybe I made a mistake. Wait, the problem says "all sectors of the spinner are the same size". Let's check the diagram again. The spinner: Blue (1), Red (1), Yellow (1), Red (2), Yellow (2). Wait, no, maybe it's 5 sectors. So red: 2, yellow: 2, blue: 1. So total sectors: 5. So (a) probability red: 2/5. (b) yellow: 2/5. (c) blue: 1/5. Wait, but let's confirm. Wait, maybe the spinner has 5 sectors? Wait, no, maybe I miscounted. Wait, the image: the spinner is divided into 5 equal parts? No, maybe 5. So for part (a), red sectors: 2, total sectors: 5. So probability is 2/5. For part (b), yellow sectors: 2, total sectors: 5, so 2/5. For part (c), blue sectors: 1, total sectors: 5, so 1/5. Wait, but let's check again. Wait, maybe the spinner has 5 sectors? Wait, no, maybe I made a mistake. Wait, the problem says "all sectors of the spinner are the same size", so each sector is equal. So let's count the number of red, yellow, blue. Red: 2, yellow: 2, blue: 1. Total: 5. So (a) 2/5, (b) 2/5, (c) 1/5.

Step1 (a): Count red sectors

Red sectors: 2, total sectors: 5 (since 2 red + 2 yellow + 1 blue = 5). Probability = 2/5.

Step1 (b): Count yellow sectors

Yellow sectors: 2, total sectors: 5. Probability = 2/5.

Step1 (c): Count blue sectors

Blue sectors: 1, total sectors: 5. Probability = 1/5.

Answer:

(a) $\frac{2}{5}$
(b) $\frac{2}{5}$
(c) $\frac{1}{5}$