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1. In the media cabinet at Jacquelyn's house, there are 7 comedy DVDs, 4 mystery DVDs, and 4 documentary DVDs. What is the probability of randomly selecting a mystery DVD from the cabinet?

Ask by Franklin Johnston. in the United States
Jan 29,2025

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Answer

The probability of randomly selecting a mystery DVD is \(\frac{4}{15}\) or approximately 26.7%.

Solution

To determine the probability of randomly selecting a **mystery DVD** from Jacquelyn's media cabinet, follow these steps: 1. **Calculate the Total Number of DVDs:** - **Comedy DVDs:** 7 - **Mystery DVDs:** 4 - **Documentary DVDs:** 4 \[ \text{Total DVDs} = 7 + 4 + 4 = 15 \] 2. **Determine the Number of Favorable Outcomes:** - **Mystery DVDs:** 4 3. **Calculate the Probability:** The probability \( P \) of selecting a mystery DVD is the ratio of the number of mystery DVDs to the total number of DVDs. \[ P(\text{Mystery DVD}) = \frac{\text{Number of Mystery DVDs}}{\text{Total Number of DVDs}} = \frac{4}{15} \] 4. **Express the Probability:** - **As a Fraction:** \(\frac{4}{15}\) - **As a Decimal:** Approximately 0.267 - **As a Percentage:** Approximately 26.7% **Conclusion:** The probability of randomly selecting a mystery DVD from the cabinet is \(\frac{4}{15}\), or about **26.7%**.

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To find the probability of selecting a mystery DVD, you can start by adding up the total number of DVDs in the cabinet. There are 7 comedy DVDs, 4 mystery DVDs, and 4 documentary DVDs, which gives us a total of 15 DVDs (7 + 4 + 4). The probability of selecting a mystery DVD is the number of mystery DVDs (4) divided by the total number of DVDs (15), resulting in a probability of 4/15 or approximately 0.267. Did you know that probability is not just a mathematical concept but also a powerful tool in daily decision-making? From predicting the weather to making choices in games and sports, we rely on probabilities to gauge outcomes and make informed decisions. Understanding the basics can help you feel more confident in taking calculated risks! When calculating probabilities, it’s common to make mistakes like forgetting to count the total number of outcomes correctly or mixing up numerator and denominator. A good tip is to carefully break down the problem step by step and double-check the numbers. Visualization, like drawing a simple chart or diagram of the situation, can also help you avoid common pitfalls!

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