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(a) Uinda is playing a role-playing game with her friends. She will roll dice to determine if her character unlocks a treasure chest. The probability of her character unlocking the treasure chest is \( \frac{13}{20} \). Find the odds in favor of her character unlocking the treasure chest. (b) A child has a box full of colored building blocks. She will choose one block without looking. The odds against choosing a blue block are \( \frac{4}{7} \). What is the probability of choosing a blue block? E. (

Ask by Ward Norton. in the United States
Jan 06,2025

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**Problem (a):** - The odds in favor of unlocking the treasure chest are **13 to 7**. **Problem (b):** - The probability of choosing a blue block is \( \frac{7}{11} \).

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The Deep Dive

To determine the odds in favor of Uinda's character unlocking the treasure chest, we can look at the ratio of successful outcomes to unsuccessful outcomes. Given the probability of unlocking the chest is \( \frac{13}{20} \), the odds in favor would be \( \frac{13}{7} \) (since \( 20 - 13 = 7 \)). So, the odds in favor of her character unlocking the treasure chest are 13 to 7! For the child choosing a blue block, if the odds against it are \( \frac{4}{7} \), this means that for every 4 times she does not choose a blue block, she chooses it 7 times. We can express the total chances as \( 4 + 7 = 11 \). Therefore, the probability of choosing a blue block is \( \frac{7}{11} \). Colorful possibilities await!

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