document.write( "Question 823556: You have 2 dimes, 6 nickels, and 7 pennies in your pocket. You randomly remove two coins without replacement.
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Algebra.Com's Answer #495626 by math-vortex(648)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Hi, there--\r\n" );
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document.write( "THE PROBLEM:\r\n" );
document.write( "You have 2 dimes, 6 nickels, and 7 pennies in your pocket. You randomly remove two coins \r\n" );
document.write( "without replacement.\r\n" );
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document.write( "A. What is the probability that both of them are nickels?\r\n" );
document.write( "B. What is the probability that the first is a nickel and the second is a dime?\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "Before you use your calculator you need to set up the solution. I assume you want to use the\r\n" );
document.write( "combinatoric method since you are using a calculator. \r\n" );
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document.write( "A. What is the probability that both coins are nickels?\r\n" );
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document.write( "This is a random sampling without replacement from a finite population (15 coins) whose \r\n" );
document.write( "elements can be classified into two mutually exclusive categories (nickels, not nickels)\r\n" );
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document.write( "X is the random variable = the result of drawing a coin from your pocket\r\n" );
document.write( "N is the population size = 15 (the total number of coins in your pocket)\r\n" );
document.write( "K is the number of \"successful\" coins = 6 nickels (these are the ones you want to draw)\r\n" );
document.write( "n is the number of draws = 2\r\n" );
document.write( "k is the number of successes = 2 (because you want to draw 2 nickels)\r\n" );
document.write( "(aCb) binomial coefficient, or counting combinations (the [nCr] button on your calculator)\r\n" );
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document.write( "The general formula for this type of probability distribution is\r\n" );
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document.write( "P(X=k) = [(KCk) * ((N-K)C(n-k))] / (NCn)\r\n" );
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document.write( "Don't freak out at all these letters. I'll explain each one in the context of your problem:\r\n" );
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document.write( "P(X=k) is P(X=2), the probability that you will draw successfully twice (two nickels.)\r\n" );
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document.write( "KCk is 6C2, or \"6 choose 2,\" because there are 6 successful coins (nickels) and you want to \r\n" );
document.write( "draw two of them. \"6 choose 2\" is the number of ways to select 2 things from a set of 6 when \r\n" );
document.write( "order doesn't matter.\r\n" );
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document.write( "(N-K)C(n-k) is 9C0, or \"9 choose 0,\" because there are 15-6=9 unsuccessful coins (not \r\n" );
document.write( "nickels) and you don't want to choose any of them.\r\n" );
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document.write( "NCn is 15C2, or \"15 choose 2,\" because there are 15 coins all together and you are choosing \r\n" );
document.write( "2 of them.\r\n" );
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document.write( "So, the probability of drawing two nickels is\r\n" );
document.write( "P(X=2) = [(6C2)*(9C0)] / (15C2) \r\n" );
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document.write( "Now we are ready for the calculator. Do this in three steps.\r\n" );
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document.write( "For 6C2, press these buttons:\r\n" );
document.write( "[6] [MATH] [<] [3] [2] [ENTER]\r\n" );
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document.write( "(You should get 15.) The [MATH] button takes you to the Math commands, and pressing the \r\n" );
document.write( "left arrow key once takes you to the PRB menu. Choosing [3] brings up the nCr function. Finish \r\n" );
document.write( "by typing [2] [ENTER] to get 15.\r\n" );
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document.write( "For 9C0, press:\r\n" );
document.write( "[9] [MATH] [<] [3] [0] [ENTER]. (You should get 1.)\r\n" );
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document.write( "For 15C2, press:\r\n" );
document.write( "[1] [5] [MATH] [<] [3] [2] [ENTER] (You should get 105.)\r\n" );
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document.write( "p(X=2) = (15)(1)/105 = 1/7\r\n" );
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document.write( "B. What is the probability that the first is a nickel and the second is a dime.\r\n" );
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document.write( "I personally would not use a calculator this this problem.\r\n" );
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document.write( "The probability of drawing a nickel, then a dime is\r\n" );
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document.write( "[probability of drawing the nickel]\r\n" );
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document.write( "P(draw nickel) = 6/15 because there are 15 coins altogether and 6 chances to pick on of them.\r\n" );
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document.write( "P(draw a dime after a nickel) = 2/14 because there are 14 coins left in your pocket and 2 of \r\n" );
document.write( "them are dimes.\r\n" );
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document.write( "P(draw nickel, then a dime = (6/15)(2/14) = 2/35\r\n" );
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document.write( "In the calculator method you have\r\n" );
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document.write( "[(6C1)*(9C0)/(15C1)] = 2/35\r\n" );
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document.write( "Hope this helps! If you have questions about any of this, email me and I'll explain further.\r\n" );
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document.write( "Mrs. Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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