Question

A spinner is divided into equal sections of pink, green, orange, white, blue and red. Eduardo spins the spinner 30 times and records the color it lands on. The table below shows his results.
pink:3
Green:5
Orange:4
White:7
Blue:5
Red:6


Which of the following statements about the experimental and theoretical probabilities is accurate?

Responses
A The theoretical probability of the spinner landing on green is equal to the experimental probability.The theoretical probability of the spinner landing on green is equal to the experimental probability.
B The theoretical probability of the spinner landing on pink is less than the experimental probability.The theoretical probability of the spinner landing on pink is less than the experimental probability.
C The theoretical probability of the spinner landing on green is greater than the experimental probability.The theoretical probability of the spinner landing on green is greater than the experimental probability.
D The theoretical probability of the spinner landing on white is greater than the experimental probability.

Answer 1

To determine the accuracy of the statements regarding the experimental and theoretical probabilities, we first need to calculate the theoretical probabilities for each color and compare them to the experimental probabilities obtained by Eduardo.

1. **Theoretical Probability**:
Since the spinner is divided into 6 equal sections (pink, green, orange, white, blue, and red), the theoretical probability for landing on any color is:

\[
\text{Theoretical Probability} = \frac{1}{6} \approx 0.1667
\]

2. **Experimental Probability**:
This is calculated based on Eduardo's results. The experimental probability for each color is:

- Pink: \( \frac{3}{30} = 0.1 \)
- Green: \( \frac{5}{30} = 0.1667 \)
- Orange: \( \frac{4}{30} = 0.1333 \)
- White: \( \frac{7}{30} = 0.2333 \)
- Blue: \( \frac{5}{30} = 0.1667 \)
- Red: \( \frac{6}{30} = 0.2 \)

Now, we compare the theoretical probabilities to the respective experimental probabilities:

- **Pink**:
- Theoretical: \( \frac{1}{6} \approx 0.1667 \)
- Experimental: \( 0.1 \)

(Theoretical > Experimental)

- **Green**:
- Theoretical: \( \frac{1}{6} \approx 0.1667 \)
- Experimental: \( 0.1667 \)

(Theoretical = Experimental)

- **Orange**:
- Theoretical: \( \frac{1}{6} \approx 0.1667 \)
- Experimental: \( 0.1333 \)

(Theoretical > Experimental)

- **White**:
- Theoretical: \( \frac{1}{6} \approx 0.1667 \)
- Experimental: \( 0.2333 \)

(Theoretical < Experimental)

- **Blue**:
- Theoretical: \( \frac{1}{6} \approx 0.1667 \)
- Experimental: \( 0.1667 \)

(Theoretical = Experimental)

- **Red**:
- Theoretical: \( \frac{1}{6} \approx 0.1667 \)
- Experimental: \( 0.2 \)

(Theoretical < Experimental)

Now, let's evaluate the given statements:

**A**: The theoretical probability of the spinner landing on green is equal to the experimental probability.
- This is **True**.

**B**: The theoretical probability of the spinner landing on pink is less than the experimental probability.
- This is **False** (Theoretical > Experimental).

**C**: The theoretical probability of the spinner landing on green is greater than the experimental probability.
- This is **False** (Theoretical = Experimental).

**D**: The theoretical probability of the spinner landing on white is greater than the experimental probability.
- This is **False** (Theoretical < Experimental).

Based on this analysis, the accurate statement is:

**A: The theoretical probability of the spinner landing on green is equal to the experimental probability.**