Answer:
Step-by-step explanation:
It is given that The probability a person is infected by a certain cold virus is 0.2 that is p=0.2, then q=1-0.2=0.8.
Now, we have to find the probability that at least one person will be affected by the cold virus, that is P(x>1).
P(x>1)=1-(P(x=0)+P(x=1))
=[tex]1-(nc_{x}p^xq^{n-x}+nc_{x}p^xq^{n-x})[/tex]
=[tex]1-(12c_{0}p^0q^{12}+12c_{1}p^1q^{11})[/tex]
=[tex]1-((0.8)^{12} +12(0.2)(0.8)^{11})[/tex]
=[tex]1-(0.8+12(0.2))(0.8)^{11}[/tex]
=[tex]1-(0.8+2.4)(0.0858)[/tex]
=[tex]1-(3.2)(0.0858)[/tex]
=[tex]1-0.274[/tex]
=[tex]0.726[/tex]
Thus, probability that at least one person will be affected by the cold virus will be=0.726.
