Question:

A bag contains 4 red, 5 white, and some yellow balls. If the probability of drawing a red ball at random is \(\frac{1}{5}\), then find the probability of drawing a yellow ball at random.

Updated On: Jun 5, 2025
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Solution and Explanation

Step 1: Understanding the problem:
We are given that a bag contains 4 red, 5 white, and some yellow balls. The probability of drawing a red ball at random is given as \( \frac{1}{5} \). We need to find the probability of drawing a yellow ball.

Step 2: Finding the total number of balls in the bag:
Let the number of yellow balls be \( y \). The total number of balls in the bag is the sum of red, white, and yellow balls, so the total number of balls is:
\[ \text{Total balls} = 4 \, (\text{red}) + 5 \, (\text{white}) + y \, (\text{yellow}) = 9 + y \] The probability of drawing a red ball is given by the ratio of red balls to the total number of balls. This probability is \( \frac{1}{5} \), so we have the equation:
\[ \frac{4}{9 + y} = \frac{1}{5} \]

Step 3: Solve for \( y \):
To solve for \( y \), cross-multiply the equation:
\[ 4 \times 5 = 1 \times (9 + y) \] \[ 20 = 9 + y \] Now, subtract 9 from both sides:
\[ y = 20 - 9 = 11 \] Thus, the number of yellow balls is \( y = 11 \).

Step 4: Finding the probability of drawing a yellow ball:
Now that we know there are 11 yellow balls, the total number of balls in the bag is:
\[ \text{Total balls} = 9 + 11 = 20 \] The probability of drawing a yellow ball is the ratio of yellow balls to the total number of balls:
\[ \text{Probability of yellow ball} = \frac{11}{20} \]

Step 5: Conclusion:
The probability of drawing a yellow ball at random is \( \frac{11}{20} \).
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