Question

a spinner is divided into four sections, each in a different color, as shown below. after the spinner is spun, the arrow points to one of the colors. which statement about possible outcomes is true? the probability that the arrow will point to blue is more than $\frac{1}{4}$. the probability that the arrow will point to blue is 1. the probability that the arrow will point to green is $\frac{1}{4}$. the probability that the arrow will point to yellow is the same as the probability that it will point to red.

Explanation:

Step1: Analyze the size of each section

The spinner is divided into four sections. The blue section is larger than \(\frac{1}{4}\) of the spinner.

Step2: Analyze the probability of each option

• For the option "The probability that the arrow will point to blue is more than \(\frac{1}{4}\)": Since the blue section is larger than \(\frac{1}{4}\) of the spinner, by the formula \(P=\frac{\text{size of the favorable section}}{\text{total size of the spinner}}\), this option is correct.
• For the option "The probability that the arrow will point to blue is \(1\)": The probability of an event is \(1\) when it is a certain event. But the arrow can point to other colors (red, yellow, green) too, so this is wrong.
• For the option "The probability that the arrow will point to green is \(\frac{1}{4}\)": The green section is smaller than \(\frac{1}{4}\) of the spinner, so this is wrong.
• For the option "The probability that the arrow will point to yellow is the same as the probability that it will point to red": The red section is larger than the yellow section, so their probabilities are not equal, and this is wrong.

Answer:

The probability that the arrow will point to blue is more than \(\frac{1}{4}\).