Question

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?

Answer 1

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:


`_(83)C_(10)*(0.2)^(10)*(0.8)^(73) \\ \\=(83!)/(10!73!)*(0.2)^(10)*(0.8)^(73) \\ \\=0.021`

Answer 2

Answer: 0.021

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 :-

`P(X)=^nC_xp^x(1-p)^(n-x)`

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

`P(X)=^(83)C_(10)(0.2)^(10)(0.8)^(73)\\\\=(83!)/(10!(83-10)!)(0.2)^(10)(0.8)^(73)=0.0209841759622\approx0.021`

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