document.write( "Question 87391: I need help understaning how to solve these types of problems...can someone show me thanks...\r
\n" ); document.write( "\n" ); document.write( "Problem #1
\n" ); document.write( "A coin is tossed 6 times. Find the probabilities of getting the following.\r
\n" ); document.write( "\n" ); document.write( "a) Exactly 3 heads\r
\n" ); document.write( "\n" ); document.write( "Problem #2
\n" ); document.write( "Quality Control A factory tests a random sample of 20 transistors
\n" ); document.write( "for defective transistors. The probability that a particular
\n" ); document.write( "transistor will be defective has been established by past
\n" ); document.write( "experience as .05.\r
\n" ); document.write( "\n" ); document.write( "a) What is the probability that there are no defective transistors
\n" ); document.write( "in the sample?\r
\n" ); document.write( "\n" ); document.write( "Problem#3
\n" ); document.write( "Flu Inoculations A flu vaccine has a probability of 80%
\n" ); document.write( "of preventing a person who is inoculated from getting the
\n" ); document.write( "flu. A county health office inoculates 83 people. Find the
\n" ); document.write( "probabilities of the following.\r
\n" ); document.write( "\n" ); document.write( "a. Exactly 10 of the people inoculated get the flu.
\n" ); document.write( "b. No more than 4 of the people inoculated get the flu.
\n" ); document.write( "c. None of the people inoculated get the flu.
\n" ); document.write( " \n" ); document.write( "
Algebra.Com's Answer #63330 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "I need help understaning how to solve these types of \r\n" );
document.write( "problems...can someone show me thanks... \r\n" );
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document.write( "I can't tell whether you are to use binomial tables, \r\n" );
document.write( "formulas, TI graphical calculator, Excel, or normal tables \r\n" );
document.write( "to approximate the binomial probabilities.  So I'll just \r\n" );
document.write( "do them all by formula.\r\n" );
document.write( "\r\n" );
document.write( "Problem #1\r\n" );
document.write( "A coin is tossed 6 times. Find the probabilities of \r\n" );
document.write( "getting the following. \r\n" );
document.write( "a) Exactly 3 heads.\r\n" );
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document.write( "First we decide what is to be called a \"success\".\r\n" );
document.write( "Here we will let a success be \"getting a head\".  \r\n" );
document.write( "The probability of getting 1 success (head) in 1 \r\n" );
document.write( "trial is \"1%2F2\".          \r\n" );
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document.write( "The probability of getting exactly x successes in \r\n" );
document.write( "n trials, where the probability of getting 1 success \r\n" );
document.write( "in 1 trial is p is given by this formula:\r\n" );
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document.write( "\"%28n%21%2F%28x%21%28n-x%29%21%29%29%28p%5Ex%29%281-p%29%5E%28n-x%29\"\r\n" );
document.write( "\r\n" );
document.write( "The probability of getting exactly 3 successes in \r\n" );
document.write( "6 trials, where the probability of getting 1 success \r\n" );
document.write( "in 1 trial is \"1%2F2\", so we substitute\r\n" );
document.write( "x=3, n=6, and p=\"1%2F2\" \r\n" );
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document.write( "\r\n" );
document.write( "\"%286%21%2F%283%21%286-3%29%21%29%29%281%2F2%29%5E3%281-1%2F2%29%5E%286-3%29\"\r\n" );
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document.write( "\"%28720%2F36%29%281%2F2%29%5E6\"\r\n" );
document.write( "\r\n" );
document.write( "\"20%281%2F2%5E6%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"20%2F64\"\r\n" );
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document.write( "5/16\r\n" );
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document.write( "Problem #2\r\n" );
document.write( "Quality Control A factory tests a random sample of \r\n" );
document.write( "20 transistors for defective transistors. The \r\n" );
document.write( "probability that a particular transistor will be \r\n" );
document.write( "defective has been established by past experience \r\n" );
document.write( "as .05.\r\n" );
document.write( "\r\n" );
document.write( "a) What is the probability that there are no defective \r\n" );
document.write( "transistors in the sample? \r\n" );
document.write( "\r\n" );
document.write( "Another binomial problem.\r\n" );
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document.write( "First we decide what is to be called a \"success\".  \r\n" );
document.write( "Here we will let a success be \"getting a good \r\n" );
document.write( "(non-defective) transistor.\"  \r\n" );
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document.write( "We are not given the probability of 1 success in 1 \r\n" );
document.write( "trial. Instead we are given the probability of 1 failure \r\n" );
document.write( "in 1 trial is ,05, so the probability of 1 success\r\n" );
document.write( "in 1 trial is 1-.05 or .95 \r\n" );
document.write( "\r\n" );
document.write( "The probability of getting exactly x successes in \r\n" );
document.write( "n trials, where the probability of getting 1 success \r\n" );
document.write( "in 1 trial is p is given by the formula as for the \r\n" );
document.write( "other problem:\r\n" );
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document.write( "\"%28n%21%2F%28x%21%28n-x%29%21%29%29%28p%5Ex%29%281-p%29%5E%28n-x%29\"\r\n" );
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document.write( "The probability of getting exactly 20 successes in \r\n" );
document.write( "20 trials. So the probability of getting 1 success \r\n" );
document.write( "in 1 trial is \".95\", so we substitute\r\n" );
document.write( "x=20, n=20, and p=\".05\" \r\n" );
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document.write( "\r\n" );
document.write( "\"+%28+20%21%2F20%21%2820-20%29%21+%29%28.95%29%5E20%281-.95%29%5E%2820-20%29+\"\r\n" );
document.write( "\r\n" );
document.write( "\"+%2820%21%2F%2820%210%21%29%29%28.95%5E20%29%28.05%5E0%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"+%281%2F0%21%29%28.95%5E20%29%281%29\"\r\n" );
document.write( "\r\n" );
document.write( "\"+%281%2F1%29%28.95%5E20%29\"\r\n" );
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document.write( "\".95%5E20\"\r\n" );
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document.write( "(((.3584859224}}}\r\n" );
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document.write( "Problem#3\r\n" );
document.write( "Flu Inoculations A flu vaccine has a probability of 80%\r\n" );
document.write( "of preventing a person who is inoculated from getting the\r\n" );
document.write( "flu. A county health office inoculates 83 people. Find the\r\n" );
document.write( "probabilities of the following. \r\n" );
document.write( "a. Exactly 10 of the people inoculated get the flu.\r\n" );
document.write( "\r\n" );
document.write( "First we decide what is to be called a \"success\".  Here \r\n" );
document.write( "we will let a success be \"not getting the flu\".  \r\n" );
document.write( "The probability of getting 1 success in 1 trial is 80% \r\n" );
document.write( "or \".8\".          \r\n" );
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document.write( "As before, the probability of getting exactly x successes \r\n" );
document.write( "in n trials, where the probability of getting 1 success \r\n" );
document.write( "in 1 trial is p is given by this formula:\r\n" );
document.write( "\r\n" );
document.write( "\"%28n%21%2F%28x%21%28n-x%29%21%29%29%28p%5Ex%29%281-p%29%5E%28n-x%29\"\r\n" );
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document.write( "We are not being asked for the probability of exactly \r\n" );
document.write( "10 successes, but are asked for exactly 10 failures.  \r\n" );
document.write( "So since there are 83 trials, we want the probability \r\n" );
document.write( "that there are 83 - 10 or 73 successes.\r\n" );
document.write( "\r\n" );
document.write( "the probability of 1 success in 1 trial is .8.\r\n" );
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document.write( "The probability of getting exactly 73 successes in 83 \r\n" );
document.write( "trials, where the probability of getting 1 success in \r\n" );
document.write( "1 trial is .8, so we substitute\r\n" );
document.write( "x=73, n=83, and p=.8 \r\n" );
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document.write( "\"%2883%21%2F%2873%21%2883-73%29%21%29%29%28.8%29%5E73%281-.8%29%5E%2883-73%29\"\r\n" );
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document.write( "\"%2883%21%2F%2873%21%2810%29%21%29%29%28.8%29%5E73%28.2%29%5E10\"\r\n" );
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document.write( "That comes out to .020984176\r\n" );
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document.write( "b. No more than 4 of the people inoculated get the flu.\r\n" );
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document.write( "This means we have either exactly 83 successes, exactly \r\n" );
document.write( "82 successes, exactly 81 successes, or exactly 80 successes.\r\n" );
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document.write( "To find P(83 or 82 or 91 or 80) we must add\r\n" );
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document.write( "P(83) + P(82) + P(81) + P(80)\r\n" );
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document.write( "I won't go through all the calculations, for they are the same:\r\n" );
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document.write( "For P(83), we use n = 83, x = 83, p = .8, that gives 9.046256972×10-9\r\n" );
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document.write( "For P(82), we use n = 83, x = 82, p = .8, that gives 1.877098322×10-7\r\n" );
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document.write( "For P(81), we use n = 83, x = 81, p = .8, that gives 1.92402578×10-6\r\n" );
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document.write( "For P(80), we use n = 83, x = 80, p = .8, that gives 1.29871717401×10-5\r\n" );
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document.write( "Adding those up gives 1.510795588×10-5\r\n" );
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document.write( "c. None of the people inoculated get the flu.\r\n" );
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document.write( "That was answered above, as that is the probability \r\n" );
document.write( "of 83 successes in 83 trials:\r\n" );
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document.write( "For P(83), we use n = 83, x = 83, p = .8, that gives 9.046256972×10-9\r\n" );
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document.write( "Edwin
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