document.write( "Question 1200773: An harbor is being attacked by n enemy planes. The harbor defense system launches two missiles at each plane, each of which independently destroys the target with a probability of p. What is the probability that at least two enemy planes will be shot down? (p = 0.71, n = 3) \n" ); document.write( "

Algebra.Com's Answer #834986 by ikleyn(52858) $\"\"$ $\"About$

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\n" ); document.write( "An harbor is being attacked by 3 enemy planes.
\n" ); document.write( "The harbor defense system launches two missiles at each plane,
\n" ); document.write( "each of which independently destroys the target with a probability of 0.71.
\n" ); document.write( "What is the probability that at least two enemy planes will be shot down?
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\n" ); document.write( "\n" ); document.write( "                        The solution is in two steps.\r
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\n" ); document.write( "\n" ); document.write( "            First step is to determine the probability for each individual plane
\n" ); document.write( "             to be shot down by at least one of the two missiles assigned for this plane.\r
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document.write( "This probability is  P =  = 0.9159   (a precise value without rounding).\r\n" );
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document.write( "    (1-0.71) is the probability that the target will not be destroyed by one missile;\r\n" );
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document.write( "     is the probability that the target will not be destroyed by two missiles;\r\n" );
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document.write( "     is the complement to it, meaning the probability that the target \r\n" );
document.write( "                         will be destroyed by at least one of the two missiles.\r\n" );
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\n" ); document.write( "\n" ); document.write( " Second step is to solve a standard binomial distribution problem.\r
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document.write( "Now we have a standard binomial distribution probability problem.\r\n" );
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document.write( "The number of trial is n= 3; the number of success trials k is at least 2 (i.e. 2 or 3);\r\n" );
document.write( "the probability of a success for each individual trial is 0.9159.\r\n" );
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document.write( "So, the final probability is\r\n" );
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document.write( "    P = P(2) + P(3) =  =  = 0.9800  (rounded).    ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved in full.\r
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