In a bombing attack, there is 50% chance that a bomb will hit the target. Atleast two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least 99% chance of completely destroying the target, is __________.

Let n is total no. of bombs being dropped <br><br>at least 2 bombs should hit. <br><br>P(x &gt; 2) $\ge$ 0.99 <br><br>$\Rightarrow$ 1 - p(x &lt; 2) $\ge$ 0.99 <br><br>$\Rightarrow$ 1 - (p(x = 0) + p(x = 1)) $\ge$ 0.99 <br><br>$\Rightarrow$ 1 - ⁿC₀${\left( {{1 \over 2}} \right)^0}{\left( {{1 \over 2}} \right)^n}$ - ⁿC₁.${\left( {{1 \over 2}} \right)^1}{\left( {{1 \over 2}} \right)^{n - 1}}$ $\ge$ 0.99 <br><br>$\Rightarrow$ 1 - ${1 \over {{2^n}}}$ - ${n \over {{2^n}}}$ $\ge$ ${{99} \over {100}}$ <br><br>$\Rightarrow$ ${1 \over {100}}$ $\ge$ ${{n + 1} \over {{2^n}}}$ <br><br>$\Rightarrow$ 2ⁿ $\ge$ 100(n + 1) <br><br>Now checking for value of n, we get <br><br>n = 11