Probability of A winning a race is `1/5` and that for B is `1/4` Probability that neither should win is

Options

A. `2/5`
B. `3/5`
C. `4/5`
D. `9/20`

Answer

To solve the problem, we need to find the probability that neither A nor B wins the race.

### Step-by-step Solution:

1. **Identify the probabilities of A and B winning**:
- Probability of A winning, \( P(A) = \frac{1}{5} \)
- Probability of B winning, \( P(B) = \frac{1}{4} \)

2. **Calculate the probabilities of A and B not winning**:
- The probability of A not winning, \( P(A') = 1 - P(A) = 1 - \frac{1}{5} = \frac{4}{5} \)
- The probability of B not winning, \( P(B') = 1 - P(B) = 1 - \frac{1}{4} = \frac{3}{4} \)

3. **Since A and B are independent events**, we can find the probability that neither A nor B wins by multiplying their individual probabilities of not winning:
\[ P(A' \cap B') = P(A') \times P(B') = \frac{4}{5} \times \frac{3}{4} \]

4. **Perform the multiplication**:
\[ P(A' \cap B') = \frac{4}{5} \times \frac{3}{4} = \frac{4 \times 3}{5 \times 4} = \frac{12}{20} = \frac{3}{5} \]

5. **Conclusion**:
The probability that neither A nor B wins the race is \( \frac{3}{5} \).

### Final Answer:
The probability that neither A nor B wins is \( \frac{3}{5} \).