To solve the problem of how many white balls were introduced into the basket, we need to analyze the information given and use the concept of probability. ### Step-by-Step Explanation 1. **Understanding the Problem**: - We have a basket containing: - 12 red balls - 16 black balls - An unknown number of white balls (let's denote this number as \( W \)). - The total number of balls in the basket is therefore \( 12 + 16 + W = 28 + W \). - The probability of picking a white ball from the basket is given as \( \frac{3}{7} \). 2. **Setting Up the Probability Equation**: - The probability of picking a white ball can be expressed as: \[ P(\text{white}) = \frac{\text{Number of white balls}}{\text{Total number of balls}} = \frac{W}{28 + W} \] - According to the problem, this probability equals \( \frac{3}{7} \): \[ \frac{W}{28 + W} = \frac{3}{7} \] 3. **Cross-Multiplying to Solve for \( W \)**: - To eliminate the fraction, we can cross-multiply: \[ 7W = 3(28 + W) \] - Expanding the right side: \[ 7W = 84 + 3W \] 4. **Rearranging the Equation**: - Now, we will isolate \( W \) by moving all terms involving \( W \) to one side: \[ 7W - 3W = 84 \] \[ 4W = 84 \] 5. **Solving for \( W \)**: - Divide both sides by 4: \[ W = \frac{84}{4} = 21 \] ### Conclusion The number of white balls introduced into the basket is **21**. ### Explanation of Other Options - **Option A (12)**: This is incorrect because substituting \( W = 12 \) into the probability equation would yield a probability of \( \frac{12}{40} = \frac{3}{10} \), which does not equal \( \frac{3}{7} \). - **Option C (28)**: If we substitute \( W = 28 \), the total number of balls becomes \( 28 + 28 = 56 \), leading to a probability of \( \frac{28}{56} = \frac{1}{2} \), which is also incorrect. - **Option D (32)**: Substituting \( W = 32 \) gives a total of \( 28 + 32 = 60 \), resulting in a probability of \( \frac{32}{60} = \frac{8}{15} \), which does not match \( \frac{3}{7} \). ### Revision Summary - The total number of balls in the basket is \( 28 + W \). - The probability of picking a white ball is given as \( \frac{W}{28 + W} = \frac{3}{7} \). - Solving the equation leads to \( W = 21 \). - The correct answer is **B. 21**.