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 graph: yellow, blue, red, green, red, green, yellow, blue – wait, no, let's count again. Wait, the spinner: looking at the colors, let's list them: yellow, blue, red, green, red, green, yellow, blue? Wait no, maybe I miscounted. Wait the spinner is divided into 8 parts? Wait no, let's see: the colors are yellow, blue, red, green, red, green, yellow, blue? Wait no, maybe 8 regions? Wait no, let's check the colors: yellow, blue, red, green, red, green, yellow, blue? Wait, no, maybe 8 equal sectors. Wait, blue appears twice? Wait the spinner: yellow, blue, red, green, red, green, yellow, blue? Wait, no, let's count the number of regions. Let's see: the spinner has 8 regions? Wait, no, maybe 8? Wait, the problem says "equally probable that the pointer will land on any one of the regions". So first, count total number of regions. Let's look at the spinner: yellow, blue, red, green, red, green, yellow, blue? Wait, no, maybe 8 regions. Wait, blue: how many? Let's see the spinner: blue is two regions? Wait the image: yellow, blue, red, green, red, green, yellow, blue. So blue: 2 regions, yellow: 2, red: 2, green: 2. Total regions: 8.

Step2: Count regions not blue

Regions not blue: total regions (8) minus blue regions (2) = 6.

Step3: Probability for one spin

Probability of landing on non - blue in one spin is number of non - blue regions divided by total regions. So $\frac{6}{8}=\frac{3}{4}$.

Step4: Probability for two spins (independent events)

Since the spins are independent, the probability that both spins land on non - blue is the product of the probabilities of each spin. So $P=\frac{3}{4}\times\frac{3}{4}=\frac{9}{16}$? Wait, no, wait the question: "find the probability that it will land on a color other than blue for each spin" when spun twice. Wait, maybe I misread. Wait the question: "If the pointer is spun twice, find the probability that it will land on a color other than blue for each spin." So each spin, probability of non - blue is $\frac{3}{4}$, and since the two spins are independent, the probability that both are non - blue is $\frac{3}{4}\times\frac{3}{4}=\frac{9}{16}$? Wait, no, wait the first part: "Find the probability that the spinner will land on a color other than blue for each spin." Wait, maybe the question is first, find the probability for one spin, then for two spins? Wait the problem has two parts? Wait the original question: first, "Find the probability that the spinner will land on a color other than blue for each spin." (type integer or simplified fraction), then maybe the two - spin probability? Wait no, the user's question: "If the pointer is spun twice, find the probability that it will land on a color other than blue for each spin." But the box is for "Find the probability that the spinner will land on a color other than blue for each spin." (one spin). Wait let's re - check.

Wait the spinner: let's count the regions correctly. Looking at the spinner: yellow, blue, red, green, red, green, yellow, blue. So total regions: 8. Blue regions: 2. So non - blue regions: 8 - 2 = 6. So probability for one spin: $\frac{6}{8}=\frac{3}{4}$.

Wait, maybe I made a mistake in counting. Let's re - examine the spinner. The spinner: yellow, blue, red, green, red, green, yellow, blue. So blue: 2, yellow: 2, red: 2, green: 2. Total 8. So non - blue: 8 - 2 = 6. So probability for one spin: 6/8 = 3/4. Then for two spins, since each spin is independent, the probability that both are non - blue is (3/4)*(3/4)=9/16. But the box is for "Find the probability that the spinner will land on a color other than blue for each spin." (maybe the probability for each spin, i.e., one spin? But the question says "spun twice" but the box is for "each spin". Wait, maybe the first part is the probability for one spin, which is 3/4, and then the two - spin is (3/4)^2 = 9/16. But the problem's box is for "Find the probability that the spinner will land on a color other than blue for each spin." (type integer or simplified fraction). So maybe the answer for one spin is 3/4, and for two spins is 9/16. Wait, let's re - read the problem:

"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.)"

Ah, maybe the first "Find the probability..." is for one spin, and then the two - spin is the main question. Wait, no, the problem is: when spun twice, find the probability that it lands on non - blue for each spin. So each spin, the probability is 3/4, and since the two spins are independent, we multiply the probabilities.

Wait, let's confirm:

Total number of regions: 8 (as each color: blue, yellow, red, green each have 2 regions: 2 + 2+2 + 2 = 8).

Number of regions not blue: 8 - 2 = 6.

Probability of non - blue in one spin: 6/8 = 3/4.

Since the two spins are independent events, the probability that both spins result in non - blue is (3/4) * (3/4) = 9/16.

But the box is for "Find the probability that the spinner will land on a color other than blue for each spin." Maybe that's the probability for one spin, which is 3/4, and then the two - spin is 9/16. Wait, the problem's wording is a bit confusing. Let's check the original problem again:

The first part: "Find the probability that the spinner will land on a color other than blue for each spin." (maybe this is the probability for one spin, which is 3/4), and then the main question is when spun twice, find the probability that it lands on non - blue for each spin (i.e., both spins), which is (3/4)^2 = 9/16.

But the box is for the first "Find the probability...", so maybe 3/4. Wait, no, 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." So "for each spin" in the context of two spins means that both spins land on non - blue. So we need to calculate the probability of non - blue in first spin and non - blue in second spin.

So step by step:

1. Total regions: 8 (as each of blue, yellow, red, green has 2 regions: 2*4 = 8).

2. Regions not blue: 8 - 2 = 6.

3. Probability of non - blue in one spin: 6/8 = 3/4.

4. Since the two spins are independent, the probability that both are non - blue is (3/4) * (3/4) = 9/16.

So the answer is 9/16.

Answer:

$\frac{9}{16}$