document.write( "Question 1162606: The probability John buys a car is .3 and the probability that Jane buys a car is .2. However if John buys a new car the probability Jane buys a car is .4.
\n" ); document.write( "Are the purchases exclusive?
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\n" ); document.write( "What is the probability that both buy a car?
\n" ); document.write( "What is the probability that a least one buys a car?
\n" ); document.write( "What is the probability neither buys a car? \n" ); document.write( "

Algebra.Com's Answer #786777 by ikleyn(52855) $\"\"$ $\"About$

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document.write( "First statement says that  P(John) = 0.3  and  P(Jane) = 0.2.\r\n" );
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document.write( "The second statement is about the conditional probability. It says\r\n" );
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document.write( "    P(John and Jane) / P(John) = 0.4,  or, equivalently,\r\n" );
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document.write( "    P(John and Jane) = 0.3*0.4 = 0.12.\r\n" );
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document.write( "Now I am ready to answer questions.\r\n" );
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document.write( "(a)  To answer this question, we must compare  P(John and Jane)  with  P(John)*P(Jane).\r\n" );
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document.write( "     P(John and JAne) = 0.12, as we saw above;  P(John)*P(Jane) = 0.3*0.2 = 0.06.\r\n" );
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document.write( "     ANSWER.  These events are NOT independent.\r\n" );
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document.write( "(b)  I just found this value:  P(John and Jane) = 0.12.\r\n" );
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document.write( "(c)  P(John or Jane) = P(John) + P(Jane) - P(John and Jane) = 0.3 + 0.2 - 0.12.\r\n" );
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document.write( "     You complete this calculation.\r\n" );
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document.write( "(d)  This probability is the complement to (c).\r\n" );
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