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6.1.2 Exam: Semester 2 Exam Question 10 of 40 Kostya randomly chooses a number from 1 to 10 . What is the probability he chooses a number less than 5 ? A. \( \frac{2}{5} \) B. \( \frac{3}{5} \) C. \( \frac{1}{2} \) D. \( \frac{4}{9} \)

Ask by Cox Reed. in the United States
Jan 31,2025

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The probability that Kostya chooses a number less than 5 is \( \frac{2}{5} \).

Solution

To determine the probability that Kostya chooses a number less than 5 from the numbers 1 to 10, follow these steps: 1. **Total Possible Outcomes**: There are 10 possible numbers Kostya can choose from (1 through 10). 2. **Favorable Outcomes**: The numbers less than 5 are 1, 2, 3, and 4. That makes 4 favorable outcomes. 3. **Calculate Probability**: \[ \text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Possible Outcomes}} = \frac{4}{10} = \frac{2}{5} \] **Answer:** **A. \( \frac{2}{5} \)**

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To find the probability that Kostya chooses a number less than 5 from the set of numbers 1 to 10, we first identify the favorable outcomes (the numbers less than 5). These numbers are 1, 2, 3, and 4, which gives us 4 favorable outcomes. The total numbers he can choose from are 10. Therefore, the probability is calculated as: \[ \text{Probability} = \frac{\text{Favorable Outcomes}}{\text{Total Outcomes}} = \frac{4}{10} = \frac{2}{5}. \] So the correct answer is A. \( \frac{2}{5} \). Remember, when dealing with probability, always divide the number of successful outcomes by the total number of possible outcomes! This way, you can clearly see the chance of any event happening. Happy calculating!

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