Amar and Bimal are two contestants for an election, probability that Amar will win is 1/4 and that Bimal will win the election is 1/5, then what is probability that either Amar or Bimal will win the election.

Options

A. `13//20`
B. `9//20`
C. `11//20`
D. None of these

Answer

To find the probability that either Amar or Bimal will win the election, we can follow these steps:

### Step 1: Identify the probabilities
- The probability that Amar will win the election is given as \( P(A) = \frac{1}{4} \).
- The probability that Bimal will win the election is given as \( P(B) = \frac{1}{5} \).

### Step 2: Calculate the probability that either Amar or Bimal wins
Since Amar and Bimal are the only two contestants, the probability that either Amar or Bimal wins can be calculated by adding their individual probabilities:

\[ P(A \text{ or } B) = P(A) + P(B) \]

### Step 3: Substitute the values
Now, substitute the values of \( P(A) \) and \( P(B) \):

\[ P(A \text{ or } B) = \frac{1}{4} + \frac{1}{5} \]

### Step 4: Find a common denominator
To add the fractions, we need a common denominator. The least common multiple of 4 and 5 is 20. Therefore, we convert the fractions:

\[ \frac{1}{4} = \frac{5}{20} \quad \text{and} \quad \frac{1}{5} = \frac{4}{20} \]

### Step 5: Add the fractions
Now we can add the two fractions:

\[ P(A \text{ or } B) = \frac{5}{20} + \frac{4}{20} = \frac{9}{20} \]

### Step 6: Conclusion
Thus, the probability that either Amar or Bimal will win the election is:

\[ \boxed{\frac{9}{20}} \]

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