Question
Victoria spins the spinner shown in the diagram 60 times. Her results are as follows:
Blue: 14
Green: 12
Orange: 6
Purple: 10
Red: 10
Yellow: 8
(2 points)
Enter your answer as a simplified fraction.
What is the theoretical probability of landing on green?
What is the experimental probability of landing on green?
Question 2
(1 point)
The theoretical probability of landing on green is
the experimental probability of landing on green.
Answers
GPT-4o mini
To find the theoretical and experimental probabilities of landing on green, we will use the definitions of both probabilities.
**Theoretical Probability:**
The theoretical probability of an event is given by the formula:
\[
P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]
Without the diagram, we can’t ascertain the exact number of sections on the spinner, but if we assume that the spinner is divided into 6 equal sections (as suggested by the counts of the colors), we can find the theoretical probability for green.
If there are 6 colors:
- Total Outcomes = 6 (Blue, Green, Orange, Purple, Red, Yellow)
- Favorable Outcomes for Green = 1 (1 section for green)
Thus, the theoretical probability of landing on green is:
\[
P(\text{Green}) = \frac{1}{6}
\]
**Experimental Probability:**
The experimental probability is calculated using the results obtained from the spins:
\[
P(\text{Green}) = \frac{\text{Number of times Green was landed on}}{\text{Total number of spins}}
\]
From the results provided:
- Number of times Green was landed on = 12
- Total spins = 60
So the experimental probability of landing on green is:
\[
P(\text{Green}) = \frac{12}{60} = \frac{1}{5} \text{ (after simplification)}
\]
**Summary:**
- Theoretical Probability of landing on green: \(\frac{1}{6}\)
- Experimental Probability of landing on green: \(\frac{1}{5}\)
**Question 2:**
The theoretical probability of landing on green is **not equal to** the experimental probability of landing on green (since \(\frac{1}{6} \neq \frac{1}{5}\)).
**Theoretical Probability:**
The theoretical probability of an event is given by the formula:
\[
P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}
\]
Without the diagram, we can’t ascertain the exact number of sections on the spinner, but if we assume that the spinner is divided into 6 equal sections (as suggested by the counts of the colors), we can find the theoretical probability for green.
If there are 6 colors:
- Total Outcomes = 6 (Blue, Green, Orange, Purple, Red, Yellow)
- Favorable Outcomes for Green = 1 (1 section for green)
Thus, the theoretical probability of landing on green is:
\[
P(\text{Green}) = \frac{1}{6}
\]
**Experimental Probability:**
The experimental probability is calculated using the results obtained from the spins:
\[
P(\text{Green}) = \frac{\text{Number of times Green was landed on}}{\text{Total number of spins}}
\]
From the results provided:
- Number of times Green was landed on = 12
- Total spins = 60
So the experimental probability of landing on green is:
\[
P(\text{Green}) = \frac{12}{60} = \frac{1}{5} \text{ (after simplification)}
\]
**Summary:**
- Theoretical Probability of landing on green: \(\frac{1}{6}\)
- Experimental Probability of landing on green: \(\frac{1}{5}\)
**Question 2:**
The theoretical probability of landing on green is **not equal to** the experimental probability of landing on green (since \(\frac{1}{6} \neq \frac{1}{5}\)).