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document.write( "Giving a test to a group of students, the grades and gender are summarized below\r
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document.write( " A B C Total\r\n" );
document.write( "Male 3 17 16 36\r\n" );
document.write( "Female 14 15 6 35\r\n" );
document.write( "Total 17 32 22 71\r\n" );
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If one student is chosen at random,
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document.write( "A. Find the probability that the student was male:
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document.write( "B. Find the probability that the student was male AND got a \"C\":
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document.write( "C. Find the probability that the student was male OR got a \"C\":
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document.write( "D. If one student is chosen at random, find the probability that the student was male GIVEN they got a C'
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document.write( "(A) The answer is obvious: take the total from the row \"Male\", which is 36, \r\n" );
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document.write( " and relate it to the global total, which is 71\r\n" );
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document.write( " P = 
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document.write( "(B) Take the number from the cell, which is intersection of the row \"Male\" \r\n" );
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document.write( " and the column \"C\". This number is 16. Relate it to the global total, which is 71\r\n" );
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document.write( " P = 
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document.write( "(C) Take total from the row \"Male\": it is 36.\r\n" );
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document.write( " Take a total from the column C: it is 22.\r\n" );
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document.write( " Add these two values and subtract the number in the intersection the row \"Male\"\r\n" );
document.write( " and column \"C\", which is 16.\r\n" );
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document.write( " So, you calculate 36 + 22 - 16 = 42. <<<---=== We subtract 16 in order for do not count it twice.\r\n" );
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document.write( " This is the number of people in the category \"male or got a C\".\r\n" );
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document.write( " Finally, relate it to the global total 71 \r\n" );
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document.write( " P = 
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document.write( "(D) This question is about the conditional probability.\r\n" );
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document.write( " Since the say \"GIVEN they got a C\", this means that in calculation this probability\r\n" );
document.write( " we can reduce our scope to column C.\r\n" );
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document.write( " In this column, we take the number from row \"Male\": this number is 16.\r\n" );
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document.write( " Finally, we relate this number 16 to the total in column C, which is 22.\r\n" );
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document.write( " The sough probability is P = 
= 
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document.write( "Solved. All question are answered with explanations.\r
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