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.

Answer 1

Step 1: Defining the variables:

Let the number of yellow balls be \( x \).
The total number of balls in the bag is the sum of the red balls, green balls, and yellow balls, which is \( 4 + 5 + x = 9 + x \).

Step 2: Setting up the probability equation:

The probability of drawing a red ball is given by the ratio of red balls to the total number of balls. The probability of drawing a red ball is also given as \( \frac{1}{5} \). Therefore, we can set up the equation:
\[ \frac{4}{9 + x} = \frac{1}{5} \]

Step 3: Solving for \( x \):

Now, we solve for \( x \) by cross-multiplying:
\[ 4 \times 5 = 1 \times (9 + x) \] \[ 20 = 9 + x \] \[ x = 20 - 9 = 11 \]

Step 4: Conclusion:

Thus, the number of yellow balls is \( x = 11 \). The total number of balls in the bag is:
\[ 9 + 11 = 20 \]

Step 5: Finding the probability of drawing a yellow ball:

The probability of drawing a yellow ball is the ratio of yellow balls to the total number of balls. Therefore, the probability of drawing a yellow ball is:
\[ \frac{11}{20} \] Thus, the probability of drawing a yellow ball is \( \frac{11}{20} \).