document.write( "Question 1197752: Sarah is deciding which courses she wants to take in her next college semester. The probability that she will enroll in an algebra course is 0.30 and the probability that she will enroll in a Biology course is 0.70. The probability that she will enroll in an Algebra course GIVEN that she enrolls in a Biology course is 0.40. (a) What is the probability that she will enroll in both Algebra and Biology courses? (b) What is the probability that she will enroll in an Algebra course OR a Biology course? (c) Are the two events independent? (d) Are the two events mutually exclusive?
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Algebra.Com's Answer #831148 by ikleyn(52794) $\"\"$ $\"About$

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\n" ); document.write( "Sarah is deciding which courses she wants to take in her next college semester.
\n" ); document.write( "The probability that she will enroll in an algebra course is 0.30 and the probability that she will enroll in a Biology course is 0.70.
\n" ); document.write( "The probability that she will enroll in an Algebra course GIVEN that she enrolls in a Biology course is 0.40.
\n" ); document.write( "(a) What is the probability that she will enroll in both Algebra and Biology courses?
\n" ); document.write( "(b) What is the probability that she will enroll in an Algebra course OR a Biology course?
\n" ); document.write( "(c) Are the two events independent?
\n" ); document.write( "(d) Are the two events mutually exclusive?
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document.write( "The problem states that\r\n" );
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document.write( "    \"The probability that she will enroll in an Algebra course GIVEN that she enrolls in a Biology course is 0.40.\" \r\n" );
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document.write( "It means that the ratio   = 0.4.\r\n" );
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document.write( "It implies  that  P(enroll both A and B) = 0.4*P(enroll B) = 0.4*0.7 = 0.28.\r\n" );
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document.write( "It is the  ANSWER  to question (a).\r\n" );
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document.write( "(b)  Having it, we calculate\r\n" );
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document.write( "         P(enroll A or B) = P(enroll A) + P(enroll B) - P(Enroll both A and B) = 0.3 + 0.7 - 0.28 = 0.72.\r\n" );
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document.write( "     It is the  ANSWER  to question (b).\r\n" );
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document.write( "(c)  To answer question (c), we compare  P(enroll both A and B)  with  P(enroll A)*P(enroll B).\r\n" );
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document.write( "     P(enroll both) is 0.28, according to (a).\r\n" );
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document.write( "     P(A)*P(B) = 0.3*0.7 = 0.21.\r\n" );
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document.write( "     As you see, values P(A and B) and P(A)*P(B) are different, so we conclude that A and B are NOT independent events.\r\n" );
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document.write( "     It is the  ANSWER  to question (c).\r\n" );
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document.write( "(d)  Since P(A and B) is not zero  (it is 0.28),  events A and B are NOT mutually exclusive.\r\n" );
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document.write( "     It is the  ANSWER  to question (d).\r\n" );
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