Question

a spinner with repeated colors numbered from 1 to 8 is shown. sections 1 and 8 are purple. sections 2 and 3 are yellow. sections 4, 5, and 6 are blue. section 7 is orange. which statement about probability is true? the probability of landing on orange is greater than the probability of landing on purple. the probability of landing on yellow is less than the probability of landing on blue. the probability of landing on orange is equal to the probability of landing on yellow. the probability of landing on purple is equal to the probability of landing on blue.

Explanation:

Step1: Calculate total sections

There are 8 sections (1 - 8), so total outcomes \( n = 8 \).

Step2: Find counts for each color

• Purple: Sections 1, 8 → \( n_{\text{purple}} = 2 \)
• Yellow: Sections 2, 3 → \( n_{\text{yellow}} = 2 \)
• Blue: Sections 4, 5, 6 → \( n_{\text{blue}} = 3 \)
• Orange: Section 7 → \( n_{\text{orange}} = 1 \)

Step3: Calculate probabilities

• \( P(\text{purple}) = \frac{2}{8} = \frac{1}{4} \)
• \( P(\text{yellow}) = \frac{2}{8} = \frac{1}{4} \)
• \( P(\text{blue}) = \frac{3}{8} \)
• \( P(\text{orange}) = \frac{1}{8} \)

Step4: Analyze each option

1. Orange (\( \frac{1}{8} \)) vs Purple (\( \frac{1}{4} \)): \( \frac{1}{8} < \frac{1}{4} \) → False.
2. Yellow (\( \frac{1}{4} = \frac{2}{8} \)) vs Blue (\( \frac{3}{8} \)): \( \frac{2}{8} < \frac{3}{8} \) → True.
3. Orange (\( \frac{1}{8} \)) vs Yellow (\( \frac{2}{8} \)): \( \frac{1}{8}

eq \frac{2}{8} \) → False.

1. Purple (\( \frac{2}{8} \)) vs Blue (\( \frac{3}{8} \)): \( \frac{2}{8}

eq \frac{3}{8} \) → False.

Answer:

The probability of landing on yellow is less than the probability of landing on blue.