three missiles are fired at target if probability of hitting the target is 4/5 5/10 and 6/10 respectively and if all misslies are fired independently. the probability that at least two missiles willhit the target is
Answers
Step-by-step explanation:
Let vector r = (x1, x2, x3) ( where xi = 1 if missile i hit the target, and xi = 0 otherwise) represent outcome of firing.
All outcomes favorable for event A = at least two missiles hit the target are:
(1, 1, 1), probability P(1 ,1, 1) = 0.4*0.5*0.6 = P(0, 0, 0)
(1, 1, 0), probability P(1 ,1, 0) = 0.4*0.5*(1-0.6) = P(1, 0, 0)
(1, 0, 1), probability P(1 ,0, 1) = 0.4*(1-0.5)*0.6 = P(0, 1, 0)
(0, 1, 1), probability P(0 ,1, 1) = (1-0.4)*0.5*0.6 = P(0, 0, 1)
Sum of probabilities in the left column gives probability P(A)
Sum of probabilities in the right column gives probability P(A') (where A' is complementary event)
P(A) = P(A') and P(A) + P(A') =1 implies 2*P(A) = 1 and P(A) = 1/2
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It is possible to get answer simpler, reformulate problem :
Three missiles are fired at a target. The probabilities of _missing_ target are (1 - 0.4) = 0.6, (1 - 0.5) = 0.5 and (1 - 0.6) = 0.4 respectively . If missiles are fired independently . What is the probability that at least 2 missiles _miss_ the target?
And we have problem with the same probabilities. Events in questions of original and reformulated problem complementary,
then sum of their probabilities is 1, and since probabilities of these events are equal answer is 1/2.
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Answer: Probability that at least two missile hit the target is 1/2.
A linear pair of angles is formed when two lines intersect. Two angles are said to be linear if they are adjacent angles formed by two intersecting lines. The measure of a straight angle is 180 degrees, so a linear pair of angles must add up to 180 degrees.
hope it helps ☺