Probability Question 323
Question: A certain type of missile hits the target with probability p=0.3. What is the least number of missiles should be fired so that there is at least an 80% probability that the target is hit?
Options:
A) 5
B) 6
C) 7
D) None of the above
Show Answer
Answer:
Correct Answer: A
Solution:
Probability of hitting the target = 0.3 If n is the no. of times that the missile is fired.
$ \therefore $ Probability of hitting at least once $ =1-{{[1-0.3]}^{n}}=0.8 $
$ {{0.7}^{n}}=0.2 $
$ n\log 0.7=\log 0.2 $
$ \Rightarrow n=4.512 $ for $ n=4;p<0.8 $ take n = 5 $
$ Hence 5 missiles should be fired so that there is at least 80% prob. That the target is hit.
BETA
