If the probability of a shooter A not hitting a target is 0.5 and that for the shooter B is 0.7, then the probability that either A or B fails to hit the target is :

Options

A. `0 . 20`
B. `0 . 35`
C. `0 . 25`
D. `0 . 85`

Answer

To find the probability that either shooter A or shooter B fails to hit the target, we can use the concept of complementary probabilities and the principle of inclusion-exclusion.

### Step-by-Step Solution:

1. **Identify the probabilities:**
- The probability that shooter A does not hit the target, \( P(A') = 0.5 \).
- The probability that shooter B does not hit the target, \( P(B') = 0.7 \).

2. **Calculate the probability that both shooters hit the target:**
- The probability that shooter A hits the target, \( P(A) = 1 - P(A') = 1 - 0.5 = 0.5 \).
- The probability that shooter B hits the target, \( P(B) = 1 - P(B') = 1 - 0.7 = 0.3 \).
- The probability that both A and B hit the target is given by:
\[ P(A \cap B) = P(A) \cdot P(B) = 0.5 \cdot 0.3 = 0.15 \]

3. **Calculate the probability that at least one of them fails to hit the target:**
- The probability that either A or B fails to hit the target is the complement of the probability that both hit the target:
\[ P(A' \cup B') = 1 - P(A \cap B) = 1 - 0.15 = 0.85 \]

4. **Conclusion:**
- Therefore, the probability that either shooter A or shooter B fails to hit the target is \( 0.85 \).

### Final Answer:
The probability that either A or B fails to hit the target is \( 0.85 \).

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