document.write( "Question 138655: If 20 students register for a Sociology class and 35 students register for Psychology, and 15 students register for both classes, if one student is selected at random, what is the probability that student only registered for Sociology or Psychology? \n" ); document.write( "

Algebra.Com's Answer #101192 by Edwin McCravy(20081) $\"\"$ $\"About$

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If 20 students register for a Sociology class and 35 students register for Psychology, and 15 students register for both classes, if one student is selected at random, what is the probability that student only registered for Sociology or Psychology?\r
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document.write( "Draw a circle which will enclose all 20 Sociology students. Label\r\n" );
document.write( "it S.\r\n" );
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document.write( "Draw another circle, overlapping the first, which will enclose\r\n" );
document.write( "all 35 Psychology students. Label it P.\r\n" );
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document.write( "The region where the two circle overlap will enclose the 15 students who\r\n" );
document.write( "registered for both classes. So we begin by writing 15 in the overlapping\r\n" );
document.write( "part to indicate that these 15 students are inside both circles.\r\n" );
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document.write( "Since the circle labeled S must contain 20 students, and 15 of these \r\n" );
document.write( "20 students are in the overlappng part, the other 20-15 or 5 students\r\n" );
document.write( "in circle S must be in the left portion of circle S.  So we write 5\r\n" );
document.write( "in the left portion of the left circle to indicate that the 5 students\r\n" );
document.write( "are located there.\r\n" );
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document.write( "Those 5 and 15 students in the left circle account for the entire 20\r\n" );
document.write( "Sociology students, the 5 taking Sociology and NOT Psychology, and\r\n" );
document.write( "the 15 taking both courses.\r\n" );
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document.write( "Now, since the circle labeled P must contain 35 students, and 15 of these \r\n" );
document.write( "35 students are in the overlappng part, the other 35-15 or 20 students\r\n" );
document.write( "in circle P must be in the right portion of circle P.  So we write 20\r\n" );
document.write( "in the right portion of the right circle to indicate that the 20 students\r\n" );
document.write( "are located there.\r\n" );
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document.write( "Now we see that we have a total of 5+15+20 or 40 students. \r\n" );
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document.write( "We are asked for the probability that a randomly selected student\r\n" );
document.write( "only registered for Sociology or Psychology.  That is, that they\r\n" );
document.write( "only registered for ONE of the two courses.\r\n" );
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document.write( "So the random student selected must be from the left or right\r\n" );
document.write( "regions and not from the middle region.\r\n" );
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document.write( "Since there are 5 students in the leftmost portion and 20 in the\r\n" );
document.write( "rightmost region, to be succesful, we must pick one of these 5+20\r\n" );
document.write( "or 25 out of the total 40.  So the desired probability is \r\n" );
document.write( "which reduces to .\r\n" );
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document.write( "Edwin

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