The probability that 'A' hits a target is 4/5 and 'B' hits the same target is 3/4. If each of them hits once. The probability that target hit only one of them is :

Question

Accepted Answer

To determine the probability that the target is hit by only one of them, we need to consider two scenarios: either 'A' hits the target and 'B' misses, or 'B' hits the target and 'A' misses.

1. **Probability that 'A' hits and 'B' misses:**
   - Probability that 'A' hits the target = $ \frac{4}{5} $
   - Probability that 'B' misses the target = $ 1 - \frac{3}{4} = \frac{1}{4} $
   - Combined probability for this scenario = $ \frac{4}{5} \times \frac{1}{4} = \frac{4}{20} $

2. **Probability that 'B' hits and 'A' misses:**
   - Probability that 'B' hits the target = $ \frac{3}{4} $
   - Probability that 'A' misses the target = $ 1 - \frac{4}{5} = \frac{1}{5} $
   - Combined probability for this scenario = $ \frac{3}{4} \times \frac{1}{5} = \frac{3}{20} $

3. **Total probability that only one of them hits the target:**
   - Add the probabilities from both scenarios: $ \frac{4}{20} + \frac{3}{20} = \frac{7}{20} $

Thus, the probability that the target is hit by only one of them is $ \frac{7}{20} $, which corresponds to Option 4.

**Explanation for why other options are incorrect:**

- **Option 1: $ \frac{3}{5} $**
  - This option suggests a probability of $ \frac{12}{20} $, which is higher than the calculated probability of $ \frac{7}{20} $. It does not accurately represent the combined scenarios of only one hitting the target.

- **Option 2: $ \frac{6}{7} $**
  - This option suggests a probability of approximately $ 0.857 $, which is significantly higher than the calculated probability. It does not match the logical calculation of the scenarios.

- **Option 3: $ \frac{7}{8} $**
  - This option suggests a probability of $ 0.875 $, which is also much higher than the calculated probability. It does not align with the probability derived from the given conditions.

Therefore, based on the calculations and logical reasoning, Option 4 ($ \frac{7}{20} $) is the correct answer.