Answer to Question #123919 in Statistics and Probability for Mubeen

Question

Q1 : Three missiles are fired at target .If the probability of hitting the

target are 0.4 ,0.5 , 0.6 respectively , if the missiles are fired independently , what is the probability .

(i)that all the missiles hit the target ?

(ii) that at least one of three hits the target ?

(iii) that exactly one hits the target?

(iv)that exactly 2 hit the target?

Answer 1

(i) Since all events are independent, we receive that the following probability:

$0.4\cdot0.5\cdot0.6=0.12$

(ii) The probability that missiles will not hit the target is:

$(1-0.4)(1-0.5)(1-0.6)=0.12$

From this we get the probability that we are looking for:

$1-0.12=0.88$

(iii) We consider the case that only the first missile will hit the target, then that only the second and then the third. After that we add all the probabilities and receive:

$0.4\cdot(1-0.5)\cdot(1-0.6)+(1-0.4)\cdot0.5\cdot(1-0.6)+(1-0.4)\cdot(1-0.5)\cdot0.6=0.08+0.12+0.18=0.38$

(iv) We know the probability that all missiles will hit the target, the probability that exactly one missile will hit the target and the probability that missiles will not hit the target. From this we receive:

$1-0.12-0.38-0.12=0.38$

Answer:(i) 0.12 (ii) 0.88 (iii) 0.38 (iv) 0.38