Question

use the spinner shown. it is equally probable that the pointer will land on any one of the regions. if the pointer lands on a borderline, spin again. if the pointer is spun twice, find the probability that it will land on a color other than blue for each spin. find the probability that the spinner will land on a color other than blue for each spin. (type an integer or a simplified fraction.)

Explanation:

Step1: Count total regions

The spinner has 8 equal regions (from the visual: blue, red, green, yellow, red, green, yellow, blue? Wait, no, looking at the spinner: let's count. The colors: blue, red, green, yellow, red, green, yellow, blue? Wait, no, the spinner is divided into 8 parts. Let's list the regions: blue (1), red (1), green (1), yellow (1), red (1), green (1), yellow (1), blue (1)? Wait, no, looking at the image: the spinner has 8 sections. Let's count the blue regions: 2 (top blue, bottom blue). So total regions \( n = 8 \).

Step2: Count non - blue regions

Regions other than blue: total regions - blue regions. Blue regions: 2. So non - blue regions \( m=8 - 2=6 \).

Step3: Calculate probability for one spin

Probability \( P=\frac{\text{Number of non - blue regions}}{\text{Total number of regions}}=\frac{6}{8}=\frac{3}{4} \).

Step4: Probability for two independent spins

Since the spins are independent, the probability that both spins land on non - blue is \( P\times P=\frac{3}{4}\times\frac{3}{4}=\frac{9}{16} \)? Wait, no, wait the question first asks "Find the probability that the spinner will land on a color other than blue for each spin." Wait, the first part: "Find the probability that the spinner will land on a color other than blue for each spin." So for each spin, it's the probability for one spin, which we calculated as \( \frac{3}{4} \). Wait, let's re - read.

Wait the problem says: "If the pointer is spun twice, find the probability that it will land on a color other than blue for each spin." Wait, no, the sub - question is "Find the probability that the spinner will land on a color other than blue for each spin." So for each single spin, the probability.

Wait total regions: let's count again. The spinner: looking at the image, the sections are: blue, red, green, yellow, red, green, yellow, blue. So 8 sections. Blue sections: 2. So non - blue: 8 - 2 = 6. So probability for one spin (land on non - blue) is \( \frac{6}{8}=\frac{3}{4} \).

Answer:

\(\frac{3}{4}\)