Question

The probability a person is infected by a certain cold virus is 0.2. If a random sample of 12 people is taken, what is the probability that at least one person will be affected by the cold virus?

Answer 1

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))

=$1-(nc_{x}p^xq^{n-x}+nc_{x}p^xq^{n-x})$

=$1-(12c_{0}p^0q^{12}+12c_{1}p^1q^{11})$

=$1-((0.8)^{12} +12(0.2)(0.8)^{11})$

=$1-(0.8+12(0.2))(0.8)^{11}$

=$1-(0.8+2.4)(0.0858)$

=$1-(3.2)(0.0858)$

=$1-0.274$

=$0.726$

Thus, probability that at least one person will be affected by the cold virus will be=0.726.