Four missiles are fired at a target. if the probabilities of hitting the target are 0.3, 0.4, 0.5 and 0.6 respectively and if the missiles are fired independently then what will be the probability. i)that all the missiles hit the target? . ii)that at least one of the four hits the target? . iii)that exactly one hits the target? . iv)that exactly 2 hit the target? .

Probability hit target P(A) = 0.3 Probability hit target P(B) = 0.4 Probability hit target P(C) = 0.5 Probability not hit target P(A) = 0.7 Probability not hit target P(B) = 0.6 Probability not hit target P(C) = 0.5
(i) That all the missiles hit the target? = P(A) . P(B) . P(C) = 0.3*0.4*0.5 = 0.06
(ii) That at least one of the four hits the target? At least one hit the target = 1 – P(no hit the target) = 1 - P(A) . P(B) . P(C) = 1 – 0.7*0.6*0.5
iii) That exactly one hits the target? exactly one hits the target = P(A).P(B).P(C)+ P(A).P(B).P(C) + P(A).P(B).P(C)
vi) That exactly 2 hit the target? = P(A).P(B).P(C)+ P(A).P(B).P(C) + P(A).P(B).P(C)