Question

A study of immunizations among school-age children in California found that some areas had rates of unvaccinated school-age children as high as 13.5%. Imagine a district in the state where 13.5% of children are unvaccinated. If three children are chosen randomly (assume they are not siblings) from this district, what is the probability that all three children have been vaccinated

Answer 1

Answer: 0.6472

Explanation:

Given: The proportion of unvaccinated school-age children = 13.5%

Then, the proportion of vaccinated school-age children :p=100%-13.5%

= 86.5% = 0.865

Total children selected :n=3

Binomial probability formula:

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

The probability that all three children have been vaccinated :

`P(X=3)=\ ^3C_3(0.865)^3(0.135)^0\\=(1)(0.647214625)\approx0.6472`

Hence, the required probability = 0.6472