There is a 20% probability that a person inoculated with a particular vaccine will get the disease anyway. a county health office inoculates 83 people. What is the probabythat exactly 10 of them will get the disease at some point their lives?

The probability is 0.021 or 2.1%.

This is a binomial distribution, since there are two outcomes (infected or not infected), the probabilities are independent of each other, and there is a fixed number of trials. This is given by:

[tex]_{83}C_{10}\times(0.2)^{10}\times(0.8)^{73} \\ \\=\frac{83!}{10!73!}\times(0.2)^{10}\times(0.8)^{73} \\ \\=0.021[/tex]

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JeanaShupp JeanaShupp · Answer 2 · 2019-08-16T21:05:02+02:00

Answer: 0.021

Step-by-step explanation:

Given : The probability that a person inoculated with a particular vaccine will get the disease anyway. : p= 20%=0.20

The total people inoculates : n= 83

The binomial probability formula :-

[tex]P(X)=^nC_xp^x(1-p)^{n-x}[/tex]

Now, the probability that exactly 10 of them will get the disease at some point their lives :-

[tex]P(X)=^{83}C_{10}(0.2)^{10}(0.8)^{73}\\\\=\dfrac{83!}{10!(83-10)!}(0.2)^{10}(0.8)^{73}=0.0209841759622\approx0.021[/tex]

Hence, the probability that exactly 10 of them will get the disease at some point their lives =0.021