document.write( "Question 1206739: A jar contains 5 pennies, 5 nickels and 5 dimes. A child selects 2 coins at random without replacement from the jar. Let X represent the amount in cents of the selected coins.\r
\n" ); document.write( "\n" ); document.write( "Round your answers to 3 decimal places.\r
\n" ); document.write( "\n" ); document.write( "Find the probability X = 10. \r
\n" ); document.write( "\n" ); document.write( "Find the probability X = 11. \n" ); document.write( "

Algebra.Com's Answer #844356 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "A jar contains 5 pennies, 5 nickels and 5 dimes.
\n" ); document.write( "A child selects 2 coins at random without replacement from the jar.
\n" ); document.write( "Let X represent the amount in cents of the selected coins.
\n" ); document.write( "Round your answers to 3 decimal places.
\n" ); document.write( "(a) Find the probability X = 10.
\n" ); document.write( "(b) Find the probability X = 11.
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document.write( "(a)  The number of all possible permutations of 5+5+5 = 15 coins taken by 2 at a time is total 15*14 = 210.\r\n" );
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document.write( "     The number of all favorable permutations giving the sum of X= 10 cents is favorable = 5*4 = 20\r\n" );
document.write( "     ( any one 5c coin and other 5c coin in any order).\r\n" );
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document.write( "     The probability of success is  P =  =  = 0.095  (rounded as requested).   ANSWER\r\n" );
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document.write( "(b)  is very similar to (a), but there are some differences.  The total permutations of two coins is 15*14 = 210 \r\n" );
document.write( "     different pairs of two coins.\r\n" );
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document.write( "     Favorable are the all the pairs  11c = 10c + 1c = 1c + 10c.  The number of such pairs/(permutations) is 5*5 + 5*5 = 25+25 = 50. \r\n" );
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document.write( "     The probability of success is  P = {{50/210}}} =  = 0.238  (rounded as requested).   ANSWER\r\n" );
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