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: Understanding the Question:
A bag contains a total of 25 balls, which are either yellow or green.
The probability of drawing a green ball is given as $\frac{3}{5}$.
We need to determine the total number of yellow balls inside the bag.

Step 2: Key Formula or Approach:
The probability of getting a green ball, $P(G)$, is given by:
\[ P(G) = \frac{\text{Number of green balls (G)}}{\text{Total number of balls (T)}} \]
The remaining balls in the bag must be yellow:
\[ \text{Number of yellow balls (Y)} = \text{Total balls (T)} - \text{Number of green balls (G)} \]

Step 3: Detailed Explanation:

• Identify the given values:
Total number of balls, $T = 25$
Probability of drawing a green ball, $P(G) = \frac{3}{5}$

• Calculate the number of green balls $G$ using the probability definition:
\[ \frac{3}{5} = \frac{G}{25} \]

• Solve for $G$:
\[ G = \frac{3 \times 25}{5} \]
\[ G = 3 \times 5 = 15 \]
There are 15 green balls in the bag.

• Calculate the number of yellow balls $Y$:
\[ Y = T - G \]
\[ Y = 25 - 15 = 10 \]


Step 4: Final Answer:
The number of yellow balls in the bag is $10$.