Question
A spinner has 16 equal-sized sections. Twelve of the sections are green.
a. What is the probability that the spinner will land on green?
b. Use words to describe the probability.
Question content area bottom
Part 1
a.
enter your response here out of 16, or StartFraction nothing Over 4 EndFraction
, or
enter your response here%
a. What is the probability that the spinner will land on green?
b. Use words to describe the probability.
Question content area bottom
Part 1
a.
enter your response here out of 16, or StartFraction nothing Over 4 EndFraction
, or
enter your response here%
Answers
GPT-4o mini
To determine the probability that the spinner will land on green, we can use the formula for probability:
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]
**Part a:**
1. The number of favorable outcomes (green sections) = 12
2. The total number of outcomes (total sections) = 16
Thus, the probability that the spinner will land on green is:
\[
\text{Probability} = \frac{12}{16}
\]
This fraction can be simplified by dividing both the numerator and denominator by 4:
\[
\frac{12 \div 4}{16 \div 4} = \frac{3}{4}
\]
So,
- The probability in fraction is \( \frac{3}{4} \).
- In terms of percentage, this can be calculated as:
\[
\frac{3}{4} \times 100 = 75\%
\]
Thus, the probability that the spinner will land on green is:
1. As a fraction: **3 out of 4**, or \( \frac{3}{4} \)
2. As a percentage: **75%**
**Part b:**
The probability of landing on green is quite high, 75%. This means that if you spin the spinner multiple times, you can expect it to land on green 75 times out of 100 spins on average. In other words, the likelihood of landing on green is favorable because a significant portion of the sections are green, making it a common result when spinning the spinner.
\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]
**Part a:**
1. The number of favorable outcomes (green sections) = 12
2. The total number of outcomes (total sections) = 16
Thus, the probability that the spinner will land on green is:
\[
\text{Probability} = \frac{12}{16}
\]
This fraction can be simplified by dividing both the numerator and denominator by 4:
\[
\frac{12 \div 4}{16 \div 4} = \frac{3}{4}
\]
So,
- The probability in fraction is \( \frac{3}{4} \).
- In terms of percentage, this can be calculated as:
\[
\frac{3}{4} \times 100 = 75\%
\]
Thus, the probability that the spinner will land on green is:
1. As a fraction: **3 out of 4**, or \( \frac{3}{4} \)
2. As a percentage: **75%**
**Part b:**
The probability of landing on green is quite high, 75%. This means that if you spin the spinner multiple times, you can expect it to land on green 75 times out of 100 spins on average. In other words, the likelihood of landing on green is favorable because a significant portion of the sections are green, making it a common result when spinning the spinner.