In a precision bombing attack, there is a `50%` chance that any one bomb will strick the target. Two direct hits are required to destroy the target completely. The number of bombs which should be dropped to give a `99%` chance or better of completely destroying the target can be

Options

A. 12
B. 11
C. 10
D. 13

Explanation

To solve the problem, we need to determine the number of bombs (n) that should be dropped to ensure at least a 99% chance of getting at least 2 hits on the target, given that each bomb has a 50% chance of hitting.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- Probability of a bomb hitting the target (p) = 0.5
- Probability of a bomb missing the target (q) = 1 - p = 0.5
- We need at least 2 hits to destroy the target.

2. **Using Binomial Distribution**:
- The number of hits (X) follows a binomial distribution: \( X \sim B(n, p) \)
- We need to find \( n \) such that \( P(X \geq 2) \geq 0.99 \).

3. **Calculating the Complement**:
- Instead of calculating \( P(X \geq 2) \), we can calculate the complement:
\[ P(X \geq 2) = 1 - P(X < 2) = 1 - (P(X = 0) + P(X = 1)) \]

4. **Calculating Probabilities**:
- The probabilities of getting 0 hits and 1 hit can be calculated using the binomial formula:
\[ P(X = k) = \binom{n}{k} p^k q^{n-k} \]
- For \( k = 0 \):
\[ P(X = 0) = \binom{n}{0} (0.5)^0 (0.5)^n = (0.5)^n \]
- For \( k = 1 \):
\[ P(X = 1) = \binom{n}{1} (0.5)^1 (0.5)^{n-1} = n \cdot (0.5)^n \]

5. **Setting Up the Inequality**:
- Now we can set up the inequality:
\[ 1 - \left((0.5)^n + n \cdot (0.5)^n\right) \geq 0.99 \]
- Simplifying gives:
\[ (0.5)^n + n \cdot (0.5)^n \leq 0.01 \]
- Factoring out \( (0.5)^n \):
\[ (0.5)^n (1 + n) \leq 0.01 \]

6. **Finding n**:
- We can test values of \( n \) to find the smallest integer that satisfies this inequality.
- For \( n = 10 \):
\[ (0.5)^{10} (1 + 10) = \frac{11}{1024} \approx 0.01074 \quad \text{(not sufficient)} \]
- For \( n = 11 \):
\[ (0.5)^{11} (1 + 11) = \frac{12}{2048} \approx 0.00586 \quad \text{(sufficient)} \]
- Therefore, \( n \) must be at least 11.

### Conclusion:
The minimum number of bombs that should be dropped to ensure at least a 99% chance of destroying the target is **11**.