document.write( "Question 764687: Quetion);- 8 out of every 10 persons who contract a certain viral infection can recover. If a group of 7 people become infected, what is the probability that exactly 3 people will recover from the infection? \n" ); document.write( "
Algebra.Com's Answer #465624 by Theo(13342)\"\" \"About 
You can put this solution on YOUR website!
p = .8 = probability that a person who gets the disease will recover.
\n" ); document.write( "q = .2 = probability that a person who gets the disease will not recover.
\n" ); document.write( "q = 1 - p
\n" ); document.write( "p(x out of n will recover) = nCx * p^x * q^(n-x)
\n" ); document.write( "n = 7
\n" ); document.write( "x = 3
\n" ); document.write( "nCx = combination formula of n! / (x! * (n-x)!)
\n" ); document.write( "formula becomes:
\n" ); document.write( "7C3 * .8^3 * .2^4 = 35 * .512 * .0016 = .028672
\n" ); document.write( "this is the probability that exactly 3 will recover.
\n" ); document.write( "the formula used is the binomial probability formula.
\n" ); document.write( "the probability of exactly 0,1,2,3,4,5,6,7 recovering is shown below:
\n" ); document.write( "
\r\n" );
document.write( "n   =	7				\r\n" );
document.write( "p   =	0.8				\r\n" );
document.write( "q   =	0.2\r\n" );
document.write( "				\r\n" );
document.write( "x		p^x	     q^(n-x)	   nCx	   p(x)\r\n" );
document.write( "\r\n" );
document.write( "0		1	     0.0000128	   1	   0.0000128\r\n" );
document.write( "1		0.8	     0.000064	   7	   0.0003584\r\n" );
document.write( "2		0.64	     0.00032	   21	   0.0043008\r\n" );
document.write( "3		0.512	     0.0016	   35	   0.028672     *****\r\n" );
document.write( "4		0.4096	     0.008	   35	   0.114688\r\n" );
document.write( "5		0.32768	     0.04	   21	   0.2752512\r\n" );
document.write( "6		0.262144     0.2	   7	   0.3670016\r\n" );
document.write( "7		0.2097152    1	           1	   0.2097152\r\n" );
document.write( "					\r\n" );
document.write( "			      total probability =  1 \r\n" );
document.write( "\r\n" );
document.write( "

\n" ); document.write( " \n" ); document.write( "
\n" );