document.write( "Question 1150018: A mathematics professor assigns two problems for homework and knows that the probability of a student solving the first problem is 0.85, the probability of solving the second is 0.45, and the probability of solving both is 0.05. (Round your answers to three decimal places.)\r
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Algebra.Com's Answer #771363 by ikleyn(52855) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "\n" ); document.write( " This problem is on CONDITIONAL PROBABILITY\r
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document.write( "Let me re-formulate the problem, to make it (and its solution) more clear.\r\n" );
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document.write( "    There is a universal set U of 100 students.\r\n" );
document.write( "    Subset  A consists of 85 students.\r\n" );
document.write( "    Subset B consists of 45 students.\r\n" );
document.write( "    Subset (A & B) consists of 5 students    //  here   (A & B) means intersection A and B\r\n" );
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document.write( "(a) Jed is from subset B. what is the probability that Jed belongs to subset A, too ?\r\n" );
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document.write( "     In other words, if you take an arbitrary student from B, what is the probability that he / (or she) \r\n" );
document.write( "     does belong to the intersection C = (A & B) ?\r\n" );
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document.write( "         The ANSWER is OBVIOUS: the probability P =  = .\r\n" );
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document.write( "     On the language of conditional probability, you are given P(B) = 0.45,  P(A & B) = 0.05, and they ask you about  P(A | B).\r\n" );
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document.write( "     By the definition of the conditional probability,  \r\n" );
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document.write( "            P(A | B) = P(A & B) / P(B) = 0.05/0.45 =  =  = ,  the same answer.\r\n" );
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document.write( "(b)  Having (a) solved by me, try to solve (b)  IN THE SAME WAY on your own.\r\n" );
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document.write( "     It is VERY similar (!)\r\n" );
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