In a bombing attack, there is 50 % chance

Question:

In a bombing attack, there is $50 \%$ chance that a bomb will hit the target. At least 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________.

Solution:

Let ' $n$ ' bombs are required, then

$1-{ }^{n} C_{1} \cdot\left(\frac{1}{2}\right)^{1}\left(\frac{1}{2}\right)^{n-1}-{ }^{n} C_{0}\left(\frac{1}{2}\right)^{0}\left(\frac{1}{2}\right)^{n} \geq \frac{99}{100}$

$\Rightarrow \frac{1}{100} \geq \frac{n+1}{2^{n}} \Rightarrow 2^{n} \geq 100(n+1) \Rightarrow n \geq 11$

Leave a comment

Close
faculty

Click here to get exam-ready with eSaral

For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.

Download Now