document.write( "Question 1210435: A home pregnancy test was given to women, then pregnancy was verified through blood tests. The following table shows the home pregnancy test results.
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\n" ); document.write( "Pregnant 63 5 68
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\n" ); document.write( "Total 69 66 135
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\n" ); document.write( "P (positive pregnant) =
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Algebra.Com's Answer #852560 by Edwin McCravy(20081)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "If you copy and paste your problem in Google, you get this solution by AI:\r\n" );
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document.write( "P(positive and pregnant) = 0.467\r\n" );
document.write( "P(pregnant | positive) = 0.913\r\n" );
document.write( "P(negative and pregnant) = 0.037\r\n" );
document.write( "P(not pregnant|negative) = 0.924\r\n" );
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document.write( "Step 1: Identify the joint probabilities\r\n" );
document.write( "The problem asks for four different probabilities based on the provided table.\r\n" );
document.write( "First, we need to calculate the joint probability of a positive test and a\r\n" );
document.write( "pregnancy, which is denoted as \r\n" );
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document.write( "P(positive and pregnant) = 63/135 = 0.46666... approximately\r\n" );
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document.write( "The numerator is the number of women who are both pregnant and had a positive\r\n" );
document.write( "test, which is 63. The denominator is the total number of women, 135.\r\n" );
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document.write( "P(positive and pregnant) = 63/135 = 0.46666... approximately\r\n" );
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document.write( "Rounding to the nearest thousandth gives 0.467\r\n" );
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document.write( "Next, we calculate the joint probability of a negative test and a pregnancy,\r\n" );
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document.write( "P(negative and pregnant) \r\n" );
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document.write( "The numerator is the number of women who are pregnant and had a negative test,\r\n" );
document.write( "which is 5. The denominator is the total number of women, 135.\r\n" );
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document.write( "P(negative and pregnant) = 5/135 = 0.03703... approximately\r\n" );
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document.write( "Rounding to the nearest thousandth gives: 0.037\r\n" );
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document.write( "Step 2: Identify and calculate the conditional probabilities\r\n" );
document.write( "The remaining two probabilities are conditional probabilities, which are\r\n" );
document.write( "calculated based on a subset of the total population.\r\n" );
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document.write( "P(pregnant|positive) = 63/69 = 0.91304... approximately\r\n" );
document.write( "Rounding to the nearest thousandth gives 0.913.\r\n" );
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document.write( "P(not pregnant|negative) is the probability of a woman being pregnant given\r\n" );
document.write( "that she had a positive test. The denominator is the total number of women with\r\n" );
document.write( "a positive test, which is 69. The numerator is the number of women who are both\r\n" );
document.write( "pregnant and had a positive test, which is 63.\r\n" );
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document.write( "P(pregnant|positive) = 63/69 = 0.91304... approximately\r\n" );
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document.write( "Rounding to the nearest thousandth gives 0.913\r\n" );
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document.write( "P(pregnant|negative) is the probability of a woman not being pregnant given that\r\n" );
document.write( "she had a negative test. The denominator is the total number of women with a\r\n" );
document.write( "negative test, which is 66. The numerator is the number of women who are both\r\n" );
document.write( "not pregnant and had a negative test, which is 61.\r\n" );
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document.write( "P(not pregnant|negative) = 61/66 = 0.92424... approximately.\r\n" );
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document.write( "Rounding to the nearest thousandth gives 0.924\r\n" );
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document.write( "Google it yourself and see if I missed anything that the AI gave.\r\n" );
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document.write( "Edwin
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