Probability Question 226
Question: The probability of a bomb hitting a bridge is $ \frac{1}{2} $ and two direct hits are needed to destroy it. The least number of bombs required so that the probability of the bridge beeing destroyed is greater then 0.9, is
Options:
A) 8
B) 7
C) 6
D) 9
Show Answer
Answer:
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{{( \frac{1}{2} )}^{n}}+{}^{n}C_1{{( \frac{1}{2} )}^{n-1}}( \frac{1}{2} )<0.1\Rightarrow 10(n+1)<2^{n} $ This gives $ n\ge 8. $
BETA
