document.write( "Question 825982: A box contains 90 good items and 10 defective items. Find the probability that a
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Algebra.Com's Answer #497832 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( "A box contains 90 good items and 10 defective items. Find the probability that a\r\n" );
document.write( "sample of 10 items has no defective items.\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "This situation can be modeled by the Binomial Probability Distribution, X~Binomial (n, p)\r\n" );
document.write( "where\r\n" );
document.write( "X is the random variable\r\n" );
document.write( "n is the sample size = 10 items\r\n" );
document.write( "k is the number of successes you are interested = 10\r\n" );
document.write( "p is the probability of success (selecting a good item) = 90/100 = 0.9\r\n" );
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document.write( "The equation for finding the probability is\r\n" );
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document.write( "P(X=k) = [nCk] * [p^k] * [(1-p)^(n-k)]\r\n" );
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document.write( "nCk is a combination, the number of ways to choose k items from a set of n items. In your\r\n" );
document.write( "problem, we have 10C10, the number of ways to choose 10 good items from a sample of 10 \r\n" );
document.write( "items.\r\n" );
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document.write( "Therefore the probability of the all ten items in the sample will be good is\r\n" );
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document.write( "P(X=10) = [10C10] * [(0.9)^10] * [(0.1)^0]\r\n" );
document.write( "P(X=10) = (1) * (0.34868) * (1)\r\n" );
document.write( "P(X=10) = 0.34868\r\n" );
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document.write( "Therefore, the probability that a sample of ten items has no defective items is 0.34868.\r\n" );
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document.write( "Hope this helps! Feel free to email if you have any questions about the solution.\r\n" );
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document.write( "Good luck with your math,\r\n" );
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document.write( "Mrs. F\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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