document.write( "Question 1162983: Two marksmen shoot at a target simultaneously. Shooter A is known to have a 70% chance
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Algebra.Com's Answer #786914 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "Two marksmen shoot at a target simultaneously. Shooter A is known to have a 70% chance
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\n" ); document.write( "What is the probability that person B hit the target?
\n" ); document.write( "(Assume that accuracies of the shots remain the same and are independent of other shots by either person.)
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document.write( "We are given that EITHER A hits the target first time  at his 5-th shot,\r\n" );
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document.write( "                  OR     B hits the target first time at his 12-th shot,\r\n" );
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document.write( "but we do not know exactly who did it first, A or B.\r\n" );
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document.write( "        Also notice that this \"OR\" is EXCLUSIVE: either A or B, but not both.\r\n" );
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document.write( "The probability that A hits the target first time with his 5-th shoot  AND  B do not hit target with his 12 shoots is  \r\n" );
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document.write( "    P(A, 5+;  B, 12-) = 0.7*(1-0.7)^4 * (1-0.4)^12 = 0.7*0.3^4 * 0.6^12 = 0.00001234.\r\n" );
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document.write( "The probability that B hits the target first time with his  12-th shoot AND  A do not hit target with his 5 shoots  is\r\n" );
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document.write( "    P(B, 12+;  A, 5-) = 0.4*(1-0.4)^11 * (1-0.7)^5 = 0.4*0.6^11 * 0.3^5 = 0.00000353.\r\n" );
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document.write( "The probability that it is A who hits the target first is  \r\n" );
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document.write( "    P(A, 5+;  B, 12-) / ( P(A, 5+;  B, 12-) + P(B, 12+;  A,5-) ) =  = 0.7778.\r\n" );
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document.write( "The probability that it is B who hits the target first is  \r\n" );
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document.write( "    P(B, 12+;  A, 5-) / ( P(A, 5+;  B, 12-) + P(B, 12+;  A,5-) ) =  = 0.2222.\r\n" );
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document.write( "ANSWER.  The probability that A hits the target first is  0.7778.\r\n" );
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document.write( "         The probability that B hits the target first is  0.2222,\r\n" );
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