document.write( "Question 145031: 1. if four coins are flipped at once, what is the probability that exactly 3 tails will come up?\r
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Algebra.Com's Answer #105858 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
1. if four coins are flipped at once, what is the probability that exactly 3 tails will come up?
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document.write( "Two ways to do the problem, depending on what you are studying.\r\n" );
document.write( "List the sample space:\r\n" );
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document.write( "{HHHH,HHHT,HHTH,HHTT\r\n" );
document.write( " HTHH,HTHT,HTTH,HTTT\r\n" );
document.write( " THHH,THHT,THTH,THTT\r\n" );
document.write( " TTHH,TTHT,TTTH,TTTT}\r\n" );
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document.write( "Now I will color the ones red which have exactly 3 tails:\r\n" );
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document.write( "{HHHH,HHHT,HHTH,HHTT\r\n" );
document.write( " HTHH,HTHT,HTTH,HTTT\r\n" );
document.write( " THHH,THHT,THTH,THTT\r\n" );
document.write( " TTHH,TTHT,TTTH,TTTT}\r\n" );
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document.write( "There are 4 out of 16, so the probabliity is \"4%2F16\" or \"1%2F4\"\r\n" );
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document.write( "Second way.  Only use this is you are studying binomial probability.\r\n" );
document.write( "Otherwise ignore it. \r\n" );
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document.write( "The formula for the probability of getting exactly x successes out of n\r\n" );
document.write( "independent trials, when the probability of getting one success in one \r\n" );
document.write( "trial is p, is\r\n" );
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document.write( "\"P%28n%2Cx%2Cp%29+=+%28n%21%2F%28r%21%28n-r%29%21%29%29%28p%29%5Er%2A%281-p%29%5E%28n-r%29\"\r\n" );
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document.write( "The formula for the probability of getting exactly 3 successes out of 4\r\n" );
document.write( "independent trials, when the probability of getting one success in one \r\n" );
document.write( "trial is \"1%2F2\", is\r\n" );
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document.write( "\"P%284%2C3%2C1%2F2%29+=+%284%21%2F%283%211%21%29%29%281%2F8%29%2A%281%2F2%29%5E%281%29\"\r\n" );
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document.write( "\"P%284%2C3%2C1%2F2%29+=+4%281%2F8%29%2A%281%2F2%29+\"\r\n" );
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document.write( "\"P%284%2C3%2C1%2F2%29+=+4%281%2F16%29+\"\r\n" );
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document.write( "\"P%284%2C3%2C1%2F2%29+=+4%2F16\"\r\n" );
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document.write( "\"P%284%2C3%2C1%2F2%29+=+1%2F4\"\r\n" );
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\n" ); document.write( "2.What is \"%28%286x%2B6y%29%2F%28x-y%29%29%2F%2818%2F%285x-5y%29%29\"
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document.write( "Write as a division:\r\n" );
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document.write( "\"%28%286x%2B6y%29%2F%28x-y%29%29\"÷\"%2818%2F%285x-5y%29%29\"\r\n" );
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document.write( "Invert the second fraction and change the division to multiplication:\r\n" );
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document.write( "\"%28%286x%2B6y%29%2F%28x-y%29%29%2A%28%285x-5y%29%2F18%29\"\r\n" );
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document.write( "Factor \"6\" out of \"6x%2B6y%29\" and \"5\" out of \"5x-5y\"  \r\n" );
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document.write( "\"%28%286%28x%2By%29%29%2F%28x-y%29%29%2A%28%285%28x-y%29%29%2F18%29\"\r\n" );
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document.write( "Cancel the \"6\" into the \"18\" getting 3, and cancel the \"%28x-y%29\"s:\r\n" );
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document.write( "            \"3\"\r\n" );
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document.write( "\"%28%28x%2By%295%29%2F3\"\r\n" );
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document.write( "\"%285%28x%2By%29%29%2F3\"\r\n" );
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document.write( "You can either leave it like that or\r\n" );
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document.write( "distribute the top out and leave it like this:\r\n" );
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document.write( "\"%285x%2B5y%29%2F3\"\r\n" );
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document.write( "Or you can write \"%285%28x%2By%29%29%2F3\" as \"5%2F3\"\"%28x%2By%29\"\r\n" );
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\n" ); document.write( "3. What is the probability of rolling two number cubes and getting the sum that is odd or a multiple of 3?
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document.write( "Here are all the ways a pair of fair dice (number cubes) can be rolled:\r\n" );
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document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
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document.write( "(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)\r\n" );
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document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)\r\n" );
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document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)\r\n" );
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document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\r\n" );
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document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)\r\n" );
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document.write( "That is the sample space.  There are 36\r\n" );
document.write( "outcomes in that sample space.\r\n" );
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document.write( "Now I will go through and color the ones\r\n" );
document.write( "red which are either an odd number or a \r\n" );
document.write( "multiple of 3)\r\n" );
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document.write( "(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)\r\n" );
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document.write( "(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)\r\n" );
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document.write( "(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)\r\n" );
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document.write( "(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)\r\n" );
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document.write( "(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)\r\n" );
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document.write( "(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)\r\n" );
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document.write( "There are 24 throws out of the 36 that are either odd or are \r\n" );
document.write( "a multiple of 3.  \r\n" );
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document.write( "24 successful ways out of 36 possible ways gives a probability\r\n" );
document.write( "of \"24%2F36\" which reduces to \"2%2F3\".\r\n" );
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document.write( "Edwin
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