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 no of bombs that must be dropped to ensure that there is atleast 99% chance of completely destroying the target is ..
Option: 1 9
Option: 2 10
Option: 3 11
Option: 4 12

Answers (1)

The probability of success in one strike is p = 1/2

probability of failure = q = 1/2

Now, the probability of r success 

\mathrm{P}(\mathrm{x}=\mathrm{r})={ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}} \cdot\left(\frac{1}{2}\right)^{\mathrm{r}} \cdot\left(\frac{1}{2}\right)^{\mathrm{n}-\mathrm{r}}={ }^{\mathrm{n}} \mathrm{C}_{\mathrm{r}}\left(\frac{1}{2}\right)^{\mathrm{n}}

From the given question \mathrm{P}(\mathrm{x} \geq 2) \geq 0.99

\begin{array}{l} \Rightarrow 1-\mathrm{P}(\mathrm{x}<2) \geq 0.99 \\ \Rightarrow 1-\mathrm{P}(\mathrm{x}=0)-\mathrm{P}(\mathrm{x}=1) \geq 0.99 \\ \Rightarrow 1-0.99 \geq \frac{1+\mathrm{n}}{2^{\mathrm{n}}} \\ \Rightarrow 2^{\mathrm{n}} \geq 100+100 \mathrm{n} \\ \text { For } \mathrm{n}=10,2^{\mathrm{n}}<100+100 \mathrm{n} \\ \text { For } \mathrm{n}=11,12,13 \\ 2^{\mathrm{n}}>100+100 \mathrm{n} \end{array}

n = 11 is the least number.

Most Viewed Questions

Preparation Products

Knockout JEE Main April 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout JEE Main May 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series JEE Main May 2021

Unlimited Chapter Wise Tests, Unlimited Subject Wise Tests, Unlimited Full Mock Tests, Get Personalized Performance Analysis Report,.

₹ 6999/- ₹ 2999/-
Buy Now
Knockout JEE Main May 2022

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Mentorship from our Experts, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 34999/- ₹ 14999/-
Buy Now
JEE Main Rank Booster 2021

Booster and Kadha Video Lectures, Unlimited Full Mock Test, Adaptive Time Table, 24x7 Doubt Chat Support,.

₹ 13999/- ₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
 
Exams
Articles
Questions