document.write( "Question 1196638: Real estate ads suggest that 52% of homes for sale have garages, 39% have swimming pools, and 10% have both features\r
\n" ); document.write( "\n" ); document.write( "a) What is the probability that a home for sale has a garage, but not a pool?
\n" ); document.write( "b) If a home for sale has a garage, what's the probability that it has a pool, too?
\n" ); document.write( "c) Are having a garage and having a pool independent events? Explain.
\n" ); document.write( "d) Are having a garage and having a pool mutually exclusive? Explain \n" ); document.write( "

Algebra.Com's Answer #829572 by ikleyn(52797) $\"\"$ $\"About$

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\n" ); document.write( "Real estate ads suggest that 52% of homes for sale have garages, 39% have swimming pools, and 10% have both features
\n" ); document.write( "a) What is the probability that a home for sale has a garage, but not a pool?
\n" ); document.write( "b) If a home for sale has a garage, what's the probability that it has a pool, too?
\n" ); document.write( "c) Are having a garage and having a pool independent events? Explain.
\n" ); document.write( "d) Are having a garage and having a pool mutually exclusive? Explain
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document.write( "(a)  P(a home has a garage, but not a pool) = P(has a garage) - P(have both) = 52% - 10% = 42%.    ANSWER\r\n" );
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document.write( "(b)  This question asks about the conditional probablity\r\n" );
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document.write( "     P(a home has a pool given that it has a garage) = P(has a pool | has a garage) =  =  = .    ANSWER\r\n" );
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document.write( "(d)  Mutually exlusive means \"no intersection\", or \"empty intersection\".\r\n" );
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document.write( "     Is the intersection empty in this problem ? - the answer is in the post.\r\n" );
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document.write( "(c)  To check if these events are independent, you should compare the numbers  \r\n" );
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document.write( "         P(garage)*P(pool), from one side, and P(both), from the other side.\r\n" );
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document.write( "     Using the given data in the post, calculate and compare.\r\n" );
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document.write( "     If the numbers are the same, then the events are independent.\r\n" );
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document.write( "     If the numbers are the different, then the events are NOT independent.\r\n" );
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\n" ); document.write( "\n" ); document.write( "In (a) and (b), you have my answers with explanations.\r
\n" ); document.write( "\n" ); document.write( "In (c) and (d), you have all needed instructions.\r
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