document.write( "Question 1152147: The probability that a new automobile has a backup camera is 0.6. The probability that a new automobile has a GPS system is 0.4. The probability that a new automobile has both a backup camera and a GPS is 0.2. If a new automobile is selected at random, find the probability that it has neither a backup camera nor a GPS. \n" ); document.write( "

Algebra.Com's Answer #774090 by ikleyn(52778) $\"\"$ $\"About$

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document.write( "We are given\r\n" );
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document.write( "    P(A) = 0.6   (the probability that a new automobile has a backup camera)\r\n" );
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document.write( "    P(B) = 0.4   (the probability that a new automobile has a GPS system)\r\n" );
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document.write( "    P(A ∩ B) = 0.2   (the probability that a new automobile has both a backup camera and a GPS)\r\n" );
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document.write( "The problem asks about  the COMPLEMENTARY probability to  the event (A U B).\r\n" );
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document.write( "Use the general formula of the probability theory\r\n" );
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document.write( "    P(A U B) = P(A) + P(B) - P(A ∩ B).\r\n" );
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document.write( "Substitute the given data\r\n" );
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document.write( "    P(A U B) = 0.6 + 0.4 - 0.2 = 0.8.\r\n" );
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document.write( "Then the COMPLEMENTARY probability is\r\n" );
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document.write( "    P' = 1 - P(A U B) = 1 - 0.8 = 0.2.\r\n" );
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document.write( "It is your ANSWER : the probability that it has neither a backup camera nor a GPS is equal to 0.2.\r\n" );
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