A bag contains 20 balls . These are of three different colours : green red and blue .A ball is chosen at random from the bag . The probability of a green ball is `(1)/(4)`. The probability of a red ball is `(2)/(5)` .
What is the probability of a blue ball ?

Answer

To find the probability of drawing a blue ball from the bag, we can follow these steps:

### Step 1: Understand the total probability
The total probability of all possible outcomes (drawing a green ball, a red ball, or a blue ball) must equal 1. Therefore, we can express this as:
\[ P(\text{Green}) + P(\text{Red}) + P(\text{Blue}) = 1 \]

### Step 2: Substitute known probabilities
We know the probabilities of drawing a green ball and a red ball:
- \( P(\text{Green}) = \frac{1}{4} \)
- \( P(\text{Red}) = \frac{2}{5} \)

Substituting these values into the equation gives:
\[ \frac{1}{4} + \frac{2}{5} + P(\text{Blue}) = 1 \]

### Step 3: Find a common denominator
To combine the fractions, we need a common denominator. The denominators are 4 and 5, and the least common multiple (LCM) of 4 and 5 is 20. We will convert each fraction:
- Convert \( \frac{1}{4} \) to have a denominator of 20:
\[ \frac{1}{4} = \frac{5}{20} \]
- Convert \( \frac{2}{5} \) to have a denominator of 20:
\[ \frac{2}{5} = \frac{8}{20} \]

### Step 4: Substitute back into the equation
Now we substitute these converted fractions back into the equation:
\[ \frac{5}{20} + \frac{8}{20} + P(\text{Blue}) = 1 \]

### Step 5: Combine the fractions
Combine the fractions on the left side:
\[ \frac{5 + 8}{20} + P(\text{Blue}) = 1 \]
This simplifies to:
\[ \frac{13}{20} + P(\text{Blue}) = 1 \]

### Step 6: Solve for \( P(\text{Blue}) \)
To find \( P(\text{Blue}) \), we subtract \( \frac{13}{20} \) from 1:
\[ P(\text{Blue}) = 1 - \frac{13}{20} \]
Convert 1 to a fraction with a denominator of 20:
\[ P(\text{Blue}) = \frac{20}{20} - \frac{13}{20} = \frac{7}{20} \]

### Final Answer
Thus, the probability of drawing a blue ball is:
\[ \boxed{\frac{7}{20}} \]