document.write( "Question 1178965: True or False: For two events A and B, suppose P(A) = 0.35, P(B) = 0.65, and P(B|A) = 0.35. Then A and B are independent. \n" ); document.write( "

Algebra.Com's Answer #808436 by ikleyn(52814) $\"\"$ $\"About$

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\n" ); document.write( "True or False: For two events A and B, suppose P(A) = 0.35, P(B) = 0.65, and P(B|A) = 0.35. Then A and B are independent.
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\n" ); document.write( "\n" ); document.write( "            From two women, @ewatrrr and @MathLover1, you have two mutually exclusive answers.\r
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\n" ); document.write( "\n" ); document.write( "            I came with my own solution (number 3 for you) to find out the correct answer.\r
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\n" ); document.write( "\n" ); document.write( "            Be patient and read my post to the end.\r
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document.write( "From given data, using the definition of the  CONDITIONAL PROBABILITY,  you have\r\n" );
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document.write( "    P(A ∩ B) = P(B|A)*P(A) = 0.35*0.35 = 0.1225.\r\n" );
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document.write( "Two events, A and B, are called  independent  if and only if  P(A ∩ B) = P(A)*P(B).\r\n" );
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document.write( "We just have the value  0.1225  for  P(A ∩ B).\r\n" );
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document.write( "Now we calculate  P(A)*P(B) = 0.35*0.65 = 0.2275,  and we see that it is different from the value of  P(A ∩ B).\r\n" );
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document.write( "HENCE,  the events A and B are  N O T  I N D E P E N D E N T.     ANSWER\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "Ignore that post which state opposite.\r
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