A) 8
B) 7
C) 6
D) 9
Correct Answer: A
Solution :
Let \[n\] be the least number of bombs required and \[X\] the number of bombs that hit the bridge. Then \[X\] follows a binomial distribution with parameter \[n\] and \[p=\frac{1}{2}.\] Now \[P(X\ge 2)>0.9\Rightarrow 1-P(X<2)>0.9\] \[\Rightarrow P(X=0)+P(X=1)<0.1\] \[\Rightarrow {}^{n}{{C}_{0}}{{\left( \frac{1}{2} \right)}^{n}}+{}^{n}{{C}_{1}}{{\left( \frac{1}{2} \right)}^{n-1}}\left( \frac{1}{2} \right)<0.1\Rightarrow 10(n+1)<{{2}^{n}}\] This gives \[n\ge 8.\]
You need to login to perform this action.
You will be redirected in
3 sec
