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

Let the number of yellow balls be \(x\).

The total number of balls in the bag is \(4 + 5 + x = 9 + x\).

The probability of drawing a red ball is given by:

\[ \frac{4}{9 + x} = \frac{1}{5} \]

Now, solve for \(x\):

\[ 4 \times 5 = 1 \times (9 + x) \implies 20 = 9 + x \implies x = 11 \]

Thus, the total number of balls is \(9 + 11 = 20\).

The probability of drawing a yellow ball is:

\[ \frac{11}{20} \]