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:

$\frac{11}{20}$