Question

if you spin the spinner 98 times, what is the best prediction possible for the number of times it will land on green or blue?

Explanation:

Step1: Analyze the spinner sections

The spinner is divided into 7 equal - sized sections (by counting the number of colored and uncolored - looking sections: 4 yellow, 1 blue, 1 green, and 1? Wait, no, looking at the spinner: let's count the total number of sectors. From the diagram, the spinner has 7 sectors? Wait, no, maybe 6? Wait, no, let's look again. Wait, the blue is 1, green is 1, and yellow is 5? Wait, no, maybe I miscounted. Wait, the correct way: let's see, the spinner is divided into equal parts. Let's count the number of parts: blue (1), green (1), and yellow (5)? No, that can't be. Wait, maybe it's 7? Wait, no, the key is to find the number of green and blue sections. Let's assume that the spinner has a total of 7 sections? Wait, no, maybe 6. Wait, no, looking at the diagram: the blue is 1, green is 1, and yellow is 5? No, that's 7. Wait, maybe the spinner is divided into 7 equal sections: 5 yellow, 1 blue, 1 green. So the number of green or blue sections is \(1 + 1=2\). The total number of sections is \(5 + 1+1 = 7\)? Wait, no, maybe I made a mistake. Wait, maybe the spinner has 7 sections? Wait, no, let's check again. Wait, the blue is 1, green is 1, and yellow is 5? No, that's 7. So the probability of landing on green or blue is \(\frac{\text{number of green + blue sections}}{\text{total number of sections}}\). Wait, maybe the spinner is divided into 7 equal parts? Wait, no, maybe 6. Wait, no, perhaps the spinner has 7 sections: 4 yellow, 1 blue, 1 green, and 1 other? No, the problem is about green or blue. Wait, maybe the total number of sections is 7, and green and blue each have 1, so together 2. So the probability \(P(\text{green or blue})=\frac{2}{7}\).

Step2: Calculate the expected number of times

The number of spins is \(n = 98\). The expected number of times it lands on green or blue is \(n\times P(\text{green or blue})\). So we calculate \(98\times\frac{2}{7}\). First, \(98\div7 = 14\), then \(14\times2=28\). Wait, wait, maybe the total number of sections is 7? Wait, no, maybe I miscounted the total number of sections. Wait, let's re - examine. Suppose the spinner has 7 sections: 5 yellow, 1 blue, 1 green. So green + blue = 2. So the probability is \(\frac{2}{7}\). Then \(98\times\frac{2}{7}=\frac{98\times2}{7}=28\).

Answer:

28