document.write( "Question 1206867: In a city school, 60% of students have blue eyes, 55% have dark hair, and 20% have neither blue eyes nor dark hair. Determine the probability that a randomly selected student will have blue eyes and dark hair.\r
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Algebra.Com's Answer #844563 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "In a city school, 60% of students have blue eyes, 55% have dark hair,
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document.write( "Since  20%  have neither blue eyes nor dark hair, we conclude that \r\n" );
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document.write( "100 -20% = 80% are those who either have blue eyes OR dark hair (or both).\r\n" );
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document.write( "So, now we have  that 60%  of students have blue eyes P(B) = 0.6, \r\n" );
document.write( "55% have dark hair  P(D) = 0.55,  and their union  (B U D)  is  80%:  P(B U D) = 0.8.\r\n" );
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document.write( "Having it and using basic formula of probability, we write\r\n" );
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document.write( "      P(B U D) = 0.8,\r\n" );
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document.write( "      P(B) + P(D) - P(B and D) = 0.8,\r\n" );
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document.write( "      0.6  + 0.55 - P(B and D) = 0.8,\r\n" );
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document.write( "      0.6 + 0.55 - 0.8 = P(B and D),\r\n" );
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document.write( "      P(B and D) = 0.35.\r\n" );
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document.write( "Therefore, the probability that a randomly selected student will have blue eyes and dark hair is\r\n" );
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document.write( "    P(B and D) = 0.35 = 35%.    ANSWER\r\n" );
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