document.write( "Question 1194098: U and V are two events. P(U_ = 0.64; P(V) = 0.36, and P(U AND V) = 0.18. Find P(U|V)
\n" ); document.write( "Please show work so I can understand how to answer the question. Thank you! \n" ); document.write( "
Algebra.Com's Answer #826208 by greenestamps(13200)\"\" \"About 
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\n" ); document.write( "The response from tutor @ikleyn shows the conditional probability formula and a full solution to the problem.

\n" ); document.write( "The response also states that the concept of conditional probability is difficult for beginners.

\n" ); document.write( "That was true for me; and I see it often among students first working with the concept.

\n" ); document.write( "So let me take a moment to try to explain why the formula is what it is.

\n" ); document.write( "The basic probability equation is
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document.write( "                            good outcomes\r\n" );
document.write( "  P(desired outcome) = ------------------------\r\n" );
document.write( "                        all possible outcomes

\n" ); document.write( "The conditional probability P(U|V) is the probability that U happens, GIVEN THAT V happens. That means the only outcomes we are considering are those in which V happens -- so the denominator of the probability fraction (\"all possible outcomes\") is P(V).

\n" ); document.write( "Then the numerator of the probability fraction (\"good outcomes\") is the probability that U ALSO happens (i.e., U and V BOTH have to happen) -- so the numerator is P(U AND V).

\n" ); document.write( "And so the conditional probability formula is
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document.write( "            P(U AND V)\r\n" );
document.write( "  P(U|V) = ---------------\r\n" );
document.write( "               P(V)
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