document.write( "Question 1144391: In a neighborhood, 80% of the families have a vegetable garden, and 25% have a vegetable garden and grow lettuce in it. Find the probability that if we select a family from those known to have a vegetable garden, they will grow lettuce in it. \n" ); document.write( "
Algebra.Com's Answer #765487 by ikleyn(52814)\"\" \"About 
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document.write( "It is about so called \"conditional probability\".\r\n" );
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document.write( "If A and B are events, the conditional probability P(A | B)   //probability of A under the condition B//  is defined in this way\r\n" );
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document.write( "    P(A | B) = P(A and B) / P(B).\r\n" );
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document.write( "P(A and B) is the probability of the event (A and B).\r\n" );
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document.write( "In your case \r\n" );
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document.write( "    event  A  is  \"family has a vegetable garden\";\r\n" );
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document.write( "    event  B  is  \"family grows lettuce in the garden\";\r\n" );
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document.write( "    event (A and B) = \"family has a vegetable garden and grow lettuce in it\".\r\n" );
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document.write( "You are given  P(A) = 0.8;   P(A and B) = 0.25, and they ask you about  P(A | B).\r\n" );
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document.write( "According to the definition,  P(A | B) = P(A and B) / P(B) = \"0.25%2F0.8\" = 0.3125.\r\n" );
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document.write( "ANSWER.  the probability that if we select a family from those known to have a vegetable garden, they will grow lettuce in it is 0.3125.\r\n" );
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\n" ); document.write( "\n" ); document.write( "When the beginners start solving such problem,  the most difficult part for them is to understand who is  (A and B).\r
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\n" ); document.write( "\n" ); document.write( "As soon as the student will get who is  (A and B)   (and who are  A  and  B  separately),  the solution becomes  OBVIOUS.\r
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\n" ); document.write( "\n" ); document.write( "On intuitive level, now you should relate 0.25 of the total population not to all population, but only to 0.8 part of it.\r
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\n" ); document.write( "\n" ); document.write( "But the key to success is to firmly know the definition of the conditional probability via an intersection.\r
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\n" ); document.write( "\n" ); document.write( "For more help,  and to see other similar solved problems,  see the lesson\r
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