Question

A bag contains 25 balls. Some of them are yellow and others are green. One ball is drawn at random. If probability of getting a green ball is $3/5$, then find the number of yellow balls.

Hint:

An alternate, faster approach uses the complementary probability.
The probability of getting a yellow ball is $1 - P(G) = 1 - \frac{3}{5} = \frac{2}{5}$.
Therefore, the number of yellow balls $= \frac{2}{5} \times 25 = 10$.

Answer 1

Step 1: Use the complement of the given probability.
Since a ball is either yellow or green, $P(\text{yellow}) = 1 - P(\text{green}) = 1 - \frac{3}{5} = \frac{2}{5}$.
Step 2: Apply this fraction to the total number of balls.
Number of yellow balls $= \frac{2}{5} \times 25$.
Step 3: Simplify.
$\frac{2}{5} \times 25 = 2 \times 5 = 10$.
\[ \boxed{10 \text{ yellow balls}} \]