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.

A spinner divided into eight equal colored sections, with one orange, two purple, two yellow, and three blue.

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.

Answer 1

Answer: Choice B

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

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Step-by-step explanation:

We have the following:

• There are 2 purple sections labeled "1" and "8". The probability of getting purple is 2/8.
• There are 2 yellow sections labeled "2" and "3". The probability of getting yellow is 2/8.
• There are 3 blue sections labeled "4", "5", and "6". The probability of getting blue is 3/8.
• There's only one orange section (labeled "7"). The probability of getting orange is 1/8.

In short,

• Probability of purple = 2/8
• Probability of yellow = 2/8
• Probability of blue = 3/8
• Probability of orange = 1/8

Normally the goal is to reduce the fractions, but in this case it's better to keep them as they are. This allows for easier comparisons of other fractions.

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Now to look through the answer choices to see which are true, and which are false.

• A) This is false because the probability of orange is 1/8, while the probability of purple is 2/8. We're twice as likely to get purple compared to orange. Statement A is backwards and therefore false.
• B) This is true. The probabilities of yellow and blue are 2/8 and 3/8 respectively. Compare the numerators to see that 2 < 3, so 2/8 < 3/8. Choice B is the final answer.
• C) This is false. We found that the probability of orange was 1/8, while the probability of yellow was 2/8. It's clear that 1/8 and 2/8 aren't equal. Or you could say
  `1 \\e 2 \rightarrow 1/8 \\e 2/8`
• D) This is false. The probabilities of purple and blue are 2/8 and 3/8 respectively. Like with choice C, it's clear that 2/8 and 3/8 aren't equal.