Suppose 7.5% of a population is infected with Herpes simplex-2 virus (HSV2).You select seven individuals at random from the population.What is the probability of finding at least one HSV2-positive individual in your sample? [Hint:First find Pr(X=0). Then make use of the fact that
(X≥1)=1-Pr(X=0).]
Answers
Given : 7.5% of a population is infected with Herpes simplex-2 virus (HSV2
select seven individuals at random from the population
To Find : Probability of finding at least one HSV2-positive individual in your sample
Solution:
7.5% of a population is infected with Herpes simplex-2 virus (HSV2
=> p = 7.5/100 = 0.075
q = 1 - 0.075 = 0.925
n = 7
P(x) = ⁿCₓ(p)ˣqⁿ⁻ˣ
Probability of finding at least one HSV2-positive
= 1 - Finding none
= 1 - P(0)
= 1 - ⁷C₀(0.075)⁰(0.925)⁷
= 1 - 0.57942
= 0.42058
Probability of finding at least one HSV2-positive individual in your sample = 0.42058
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