Select the spinner that possesses all the following characteristics: Landing on 1, 2, 3, or 4 is certain It is more likely to land on 2 than not It is three times as likely to land on 4 than 1
Question
Select the spinner that possesses all the following characteristics: Landing on 1, 2, 3, or 4 is certain It is more likely to land on 2 than not It is three times as likely to land on 4 than 1
Solution
To answer this question, we need to consider the characteristics one by one:
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"Landing on 1, 2, 3, or 4 is certain": This means the spinner only has these four numbers.
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"It is more likely to land on 2 than not": This means the probability of landing on 2 is more than 50%.
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"It is three times as likely to land on 4 than 1": This means the probability of landing on 4 is three times the probability of landing on 1.
Considering these characteristics, the spinner should be divided into parts that represent the probabilities of landing on each number. Let's say the spinner is divided into 100 parts for simplicity.
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Since landing on 2 is more likely than not, let's assign more than 50 parts to 2. For example, we can assign 51 parts to 2.
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Now, we have 49 parts left for 1, 3, and 4.
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Since landing on 4 is three times as likely as landing on 1, we can assign 3 parts to 4 for every 1 part we assign to 1. If we assign 9 parts to 1, we can assign 27 parts to 4 (3 times 9).
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This leaves us with 13 parts, which we can assign to 3.
So, the spinner that meets all the characteristics is a spinner that is divided into 100 parts, with 51 parts for 2, 27 parts for 4, 13 parts for 3, and 9 parts for 1.
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