To solve this problem, we need to understand two key probabilities:
1. The probability that a person will die in the next year.
2. The probability that a person will not die in the next year.
1. Probability that a person will die in the next year:
This is given as [tex]\(\frac{814}{100,000}\)[/tex]. We can convert this fraction into a decimal to make it easier to use in further calculations. This fraction can be simplified to:
[tex]\[
\frac{814}{100,000} = 0.00814
\][/tex]
So, the probability that a person will die in the next year is:
[tex]\[
0.00814
\][/tex]
2. Probability that a person will not die in the next year:
The probability that a person will not die in the next year is complementary to the probability of dying. In other words, if we subtract the probability of dying from 1 (since the total probability must add up to 1), we'll get the probability of not dying.
So, we calculate:
[tex]\[
\text{Probability of not dying} = 1 - \text{Probability of dying}
\][/tex]
Using the calculated probability of dying:
[tex]\[
\text{Probability of not dying} = 1 - 0.00814
\][/tex]
Carrying out the subtraction:
[tex]\[
\text{Probability of not dying} = 0.99186
\][/tex]
Thus, the probability that the person will not die in the next year is:
[tex]\[
0.99186
\][/tex]
Therefore, the correct answer to the question is:
[tex]\[ \boxed{0.99186} \][/tex]
