document.write( "Question 1180343: A few people who have a particular disease take part in a medical trial that tests the effect of a medicine on the disease. Half the people are given medicine and the other half are given sugar pills, which have no effect on the disease. The medicine has a 60% chance of curing someone, but people who do not get the medicine still have a 10% chance of getting well.\r
\n" ); document.write( "\n" ); document.write( "The probability that a person gets well is ? %
\n" ); document.write( "The probability that the person was cured because of the medicine is ? %
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Algebra.Com's Answer #810020 by math_tutor2020(3817)\"\" \"About 
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\n" ); document.write( "Let's say that 1000 people are in the medical trial. Half (500) are given the actual medicine, while the other 500 are given the placebo sugar pill.\r
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\n" ); document.write( "\n" ); document.write( "Of the 500 people who took the actual medicine, we have 60% of them getting better. So we had 0.60*500 = 300 people get better. The remaining 200 unfortunately didn't get cured even though they took the actual medicine.\r
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\n" ); document.write( "\n" ); document.write( "Of those who took the sugar pill, 10% got better. So we have 0.10*500 = 50 people get better in this group while the remaining 500-50 = 450 did not get better.\r
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\n" ); document.write( "\n" ); document.write( "It's recommended you make up a table (shown below) to help organize the results. This step is optional of course.
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CuredNot CuredTotal
Took Medicine300200500
Took Sugar Pill50450500
Total3506501000
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\n" ); document.write( "\n" ); document.write( "In the table, we see that 300 got cured from the actual medicine, and 50 got cured from the placebo leading to 300+50 = 350 cured overall. The probability of a cure is 350/1000 = 0.35 = 35%
\n" ); document.write( "That takes care of the first part. \r
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\n" ); document.write( "\n" ); document.write( "Now onto the second part. Focus on the first column only. We have 300 people cured because of the medicine out of 350 cures total.
\n" ); document.write( "We then get 300/350 = 0.85714 approximately, which converts to 85.71% roughly.
\n" ); document.write( "This represents the percentage of people who got cured, and also got the actual medicine. \r
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\n" ); document.write( "\n" ); document.write( "Answers:
\n" ); document.write( "The probability that a person gets well is 35%
\n" ); document.write( "The probability that the person was cured because of the medicine is 85.71% (approximate)
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