Answer :
Answer:
The probability that the combined sample tests positive for the virus is 0.058 approximately.
Step-by-step explanation:
Consider the provided information.
It is given that the probability of infected with a certain virus is 0.002.
This can be written as:
p = probability of infected with virus = 0.002.
The probability of not infected with virus is:
q = probability of not infected with virus = 1 - p = 0.998
Blood samples from 30 people are combined.
Therefore the value of n is 30.
It is given that the combined sample tests positive if at least one person has the virus.
This can be written as:
[tex]P(x>0)=1-P[x=0][/tex]
Where x is the number of people infected with virus.
[tex]P(x>0)=1-\binom{30}{0}(0.002)^0\times (0.998)^{30}\\P(x>0)\approx1-0.942\\P(x>0)=0.058[/tex]
0.058 means that the probability is 5% that the combined test will be positive.
So, it is not unlikely for the combined sample tests positive for the virus.