A bag contains 20 coloured balls . 8 are red , 6 are blue ,3 are green ,2 are white and 1 is brown. A ball is chosen at random from the bag . What is the probability that ball chosen is :
green or white or brown ?

Answer

To solve the problem, we need to find the probability of selecting a ball that is either green, white, or brown from a bag containing a total of 20 colored balls.

### Step-by-Step Solution:

1. **Identify the Total Number of Balls:**
The total number of balls in the bag is given as 20.

2. **Identify the Number of Favorable Outcomes:**
We need to find the number of balls that are either green, white, or brown:
- Number of green balls = 3
- Number of white balls = 2
- Number of brown balls = 1

Now, we add these numbers together to find the total number of favorable outcomes:
\[ \text{Total favorable outcomes} = \text{Number of green balls} + \text{Number of white balls} + \text{Number of brown balls} = 3 + 2 + 1 = 6 \]

3. **Calculate the Probability:**
The probability \( P \) of an event is given by the formula:
\[ P(\text{event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}} \]
Substituting the values we found:
\[ P(\text{green or white or brown}) = \frac{6}{20} \]

4. **Simplify the Probability:**
We can simplify \( \frac{6}{20} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 2:
\[ P(\text{green or white or brown}) = \frac{6 \div 2}{20 \div 2} = \frac{3}{10} \]

5. **Final Answer:**
The probability that the ball chosen is green, white, or brown is:
\[ \frac{3}{10} \]