Question 764687
p = .8 = probability that a person who gets the disease will recover.
q = .2 = probability that a person who gets the disease will not recover.
q = 1 - p
p(x out of n will recover) = nCx * p^x * q^(n-x)
n = 7
x = 3
nCx = combination formula of n! / (x! * (n-x)!)
formula becomes:
7C3 * .8^3 * .2^4 = 35 * .512 * .0016 = .028672
this is the probability that exactly 3 will recover.
the formula used is the binomial probability formula.
the probability of exactly 0,1,2,3,4,5,6,7 recovering is shown below:
<pre>
n   =	7				
p   =	0.8				
q   =	0.2
				
x		p^x	     q^(n-x)	   nCx	   p(x)

0		1	     0.0000128	   1	   0.0000128
1		0.8	     0.000064	   7	   0.0003584
2		0.64	     0.00032	   21	   0.0043008
3		0.512	     0.0016	   35	   0.028672     *****
4		0.4096	     0.008	   35	   0.114688
5		0.32768	     0.04	   21	   0.2752512
6		0.262144     0.2	   7	   0.3670016
7		0.2097152    1	           1	   0.2097152
					
			      total probability =  1 

</pre>