document.write( "Question 1206244: Suppose that
\n" ); document.write( "P(A) = 0.3
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\n" ); document.write( "P(A ∩ B) = 0.06.
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\n" ); document.write( "P(B|A). \n" ); document.write( "

Algebra.Com's Answer #843541 by greenestamps(13200) $\"\"$ $\"About$

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document.write( "The basic definition of probability is this:\r\n" );
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document.write( "               # of ways event can happen\r\n" );
document.write( "  P(event) = ------------------------------\r\n" );
document.write( "              total # of possible outcomes\r\n" );
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document.write( "By definition, P(B|A) is the probability that B happens, given that A happens.\r\n" );
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document.write( "With that definition, the denominator of the probability fraction is the probability that A happens, because the only part of the sample space you are concerned with is the outcomes in which A happens.  And the numerator is the probability that both A and B happen:\r\n" );
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document.write( "            P(A ∩ B)\r\n" );
document.write( "  P(B|A) = ----------\r\n" );
document.write( "              P(A)\r\n" );
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document.write( "In your problem, the given information is the numerator and denominator of this fraction, so\r\n" );
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document.write( "            .06\r\n" );
document.write( "  P(B|A) = ----- = 0.2\r\n" );
document.write( "            0.3

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