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:

You can also find the probability of getting a yellow ball first: \(P(\text{Yellow}) = 1 - P(\text{Green}) = 1 - 3/5 = 2/5\). Then, number of yellow balls = \(2/5 \times 25 = 10\).

Answer 1

Step 1: Understanding the Concept:
Probability of an event is the ratio of the number of favorable outcomes to the total number of outcomes.
Step 2: Key Formula or Approach:
\[ P(E) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Step 3: Detailed Explanation:
Total number of balls in the bag = 25.
Let the number of green balls be \(G\).
Given, \(P(\text{Green ball}) = \frac{3}{5}\).
\[ \frac{G}{25} = \frac{3}{5} \]
Cross-multiplying to find \(G\):
\[ G = \frac{3}{5} \times 25 = 3 \times 5 = 15 \]
The number of green balls is 15.
Since the rest are yellow balls, the number of yellow balls is:
\[ \text{Number of yellow balls} = \text{Total balls} - \text{Green balls} \]
\[ \text{Number of yellow balls} = 25 - 15 = 10 \]
Step 4: Final Answer:
The number of yellow balls is 10.