document.write( "Question 998876: If 20% of patients treated with a type of malaria drug suffered bad reaction, find the probability in the treatment of 10 patients, 2 will suffer a bad reaction. \n" ); document.write( "
Algebra.Com's Answer #616617 by mathmate(429)\"\" \"About 
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\n" ); document.write( "Problem:
\n" ); document.write( "20% of patients treated with a drug suffered from bad reactions.
\n" ); document.write( "Find probability of exactly 2 out of ten randomly chosen patients will have bad reactions after being treated with the drug.
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\n" ); document.write( "Solution:
\n" ); document.write( "The problem fits in the binomial distribution because:
\n" ); document.write( "1. Trials are Bernoulli (exactly two possible outcomes, true or false)
\n" ); document.write( "2. Number of trials (n=10) is known.
\n" ); document.write( "3. All trials are assumed independent and random.
\n" ); document.write( "4. Probability of bad reaction (p=0.20) remains constant throughout the trials.\r
\n" ); document.write( "\n" ); document.write( "Let r=number of bad reactions out of n=10 trials.
\n" ); document.write( "p=0.20 (20%).
\n" ); document.write( "C(n,r)=number of combinations of n objects taken r at a time
\n" ); document.write( "=n!/(r!(n-r)!)
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\n" ); document.write( "Then the binomial distribution gives
\n" ); document.write( "P(n,r,p)=C(n,r)*p^r*(1-p)^(n-r)
\n" ); document.write( "Substituting values,
\n" ); document.write( "P(10,2,0.2)=C(10,2)*(0.2^2)*((1-0.2)^(10-2))
\n" ); document.write( "=45(0.20^2)(0.8^8)
\n" ); document.write( "=0.302 (approximately) \n" ); document.write( "
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