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 complementary probability instead of finding green balls first.
Since a ball is either yellow or green, $P(\text{yellow}) = 1 - P(\text{green})$.
Step 2: Compute the probability of yellow directly. \[ P(\text{yellow}) = 1 - \frac{3}{5} = \frac{2}{5} \]
Step 3: Apply this to the total number of balls. \[ \text{Number of yellow balls} = \frac{2}{5} \times 25 = 10 \]
\[ \boxed{10} \]