Let's find the probability that a resident is in the age group 60-69. We'll use the partially filled contingency table provided to assist us in calculating this probability.
First, let's examine the table:
\begin{center}
\begin{tabular}{|l|c|c|c|l|}
\hline & [tex]$60-69$[/tex] & [tex]$70-79$[/tex] & Over 79 & Total \\
\hline Male & 0.17 & 0.1 & 0.13 & \\
\hline Female & 0.2 & 0.2 & 0.2 & \\
\hline Total & & & & 1 \\
\hline
\end{tabular}
\end{center}
We are interested in the total probability that a resident falls in the age group 60-69.
From the table, we have:
- The probability that a male resident is in the age group 60-69: [tex]\( P(Male \cap 60-69) = 0.17 \)[/tex]
- The probability that a female resident is in the age group 60-69: [tex]\( P(Female \cap 60-69) = 0.2 \)[/tex]
The probability of being in the age group 60-69, regardless of gender, is the sum of the two probabilities:
[tex]\[ P(60-69) = P(Male \cap 60-69) + P(Female \cap 60-69) \][/tex]
Substituting the given values:
[tex]\[ P(60-69) = 0.17 + 0.2 = 0.37 \][/tex]
Therefore, the probability that a resident is in the age group 60-69 is [tex]\(0.37\)[/tex].
Given the choices:
a. 0.385
b. 0.35
c. 0.37
d. 0.4
The best answer is:
c. 0.37
