document.write( "Question 1120141: Ten balls numbered 1 to 10 are in a jar. Jack reaches into the jar and randomly removes one of the balls. Then Jill reaches into the jar and randomly removes a different ball. What is the probability that the sum of the two numbers on the balls removed is even? \n" ); document.write( "

Algebra.Com's Answer #735806 by ikleyn(52797) $\"\"$ $\"About$

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\n" ); document.write( "Let me reformulate the problem in more precise / (more correct) form:\r
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document.write( "    Ten balls numbered 1 to 10 are in a jar. Jack reaches into the jar and randomly removes two of the balls. \r\n" );
document.write( "    What is the probability that the sum of the two numbers on the balls removed is even?\r\n" );
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\n" ); document.write( "\n" ); document.write( " This phrase \"Then Jill reaches into the jar and randomly removes a different ball.\" of the original condition is not necessary . . . \r
\n" ); document.write( "\n" ); document.write( " He FOR SURE will remove a different ball, since he does not replace the first one . . . \r
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document.write( "The number of all combinations of pairs of the balls is   =  = 45.\r\n" );
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document.write( "The favorable events happen when both the balls in a pair are even,  OR when both the balls in a pair are odd.\r\n" );
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document.write( "The even numbers from 1 to 10 are  2, 4, 6, 8  and  10.\r\n" );
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document.write( "The number of combinations where both balls are even is  =  = 10.\r\n" );
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document.write( "The odd numbers from 1 to 9 are  1, 3, 5, 7, and 9.\r\n" );
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document.write( "The number of combinations where both balls are odd is  =  = 10.\r\n" );
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document.write( "Thus of 45 possible outcomes, only 10 + 10 = 20 are favorable.\r\n" );
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document.write( "Hence, the probability under the question is   = .\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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