document.write( "Question 1164160: In a pet store, a customer is randomly selected. It was determined that the probability that they owned a dog was 60% and the probability they owned a cat was 50%. The probability that the customer owner both a cat and a dog was 23%. Are the events “owning a cat” and “owning a dog” independent or dependent events? Justify answer. \r
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Algebra.Com's Answer #788464 by Edwin McCravy(20060) $\"\"$ $\"About$

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In a pet store, a customer is randomly selected. It was determined that the
\n" ); document.write( "probability that they owned a dog was 60% and the probability they owned a
\n" ); document.write( "cat was 50%. The probability that the customer owner both a cat and a dog
\n" ); document.write( "was 23%. Are the events “owning a cat” and “owning a dog” independent or
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document.write( "Two events are independent if the probability of either one is not changed\r\n" );
document.write( "when we know the probability of the other.  That is, they will be\r\n" );
document.write( "independent if\r\n" );
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document.write( "P(D|C) = P(D) and P(C|D) = P(C)\r\n" );
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document.write( "         P(D and C)    0.23 \r\n" );
document.write( "P(D|C) = ——————————  = ———— = 0.46\r\n" );
document.write( "            P(C)       0.50 \r\n" );
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document.write( "But P(D) = 0.60\r\n" );
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document.write( "So the probability of owning a dog is reduced if it is known that they own\r\n" );
document.write( "a cat.  So they are not independent.\r\n" );
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document.write( "We might as well investigate P(C|D)\r\n" );
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document.write( "P(C|D) = P(C)\r\n" );
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document.write( "         P(C and D)    0.23 \r\n" );
document.write( "P(C|D) = ——————————  = ———— = 0.3833...\r\n" );
document.write( "            P(D)       0.60 \r\n" );
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document.write( "But P(C) = 0.50\r\n" );
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document.write( "So also the probability of owning a cat is reduced if it is known that they\r\n" );
document.write( "own a dog.  So they are not independent.  So they are dependent.\r\n" );
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document.write( "Such dependent events are sometimes called \"mutually restrictive\", which\r\n" );
document.write( "means that the probability is less when the other is given.\r\n" );
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document.write( "Events are sometimes called \"mutually supportive\" if the probability is\r\n" );
document.write( "greater when the other is given.\r\n" );
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document.write( "There is a shortcut which is too cookbook for me, even though it is given in\r\n" );
document.write( "every textbook, because it's quick and it works. I don't like it because it\r\n" );
document.write( "doesn't teach you anything.  That way is:\r\n" );
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document.write( "Two events are independent if the probability that they own both equals the\r\n" );
document.write( "product of the probabilities that they own each:\r\n" );
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document.write( "So P(D)•P(C) = (0.60)•(0.50) = 0.30 but P(D and C) = 0.23.  Those are not\r\n" );
document.write( "equal so the events are dependent.\r\n" );
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document.write( "But it doesn't tell us what it really means for two events to be mutually\r\n" );
document.write( "exclusive, merely restrictive, mutually independent, mutually supportive or\r\n" );
document.write( "mutually guaranteeing.  It's just a cookbook rule that works.  \r\n" );
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document.write( "Edwin

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