Conditional Probability Question 8

calculator allowed In 2020, a survey was conducted among a randomly chosen same of adults aged 18 or greater in the United States about their preference to live in a warm climate or a cool climate. The table below displays a summary of the survey results.

\footnotesize \begin{array}{|c} \hline \text{Age} \\ \hline 18-25 \text{ years old} \\ \hline 26-60 \text{ years old} \\ \hline \text{Greater than } 65\text{ years old} \\ \hline \text{Total} \\ \hline \end{array} \begin{array}{|c|c|c|c|} \hline \text{Warm} & \text{Cool} & \text{No preference} & \text{Total} \\ \hline 155 &74& 111& 340 \\ \hline 47 &124& 154& 325 \\ \hline 89 & 165 & 121& 375 \\ \hline 291 &363& 386& 1{,}040 \\ \hline \end{array}

Which of the following is closest to the difference between the percentage of adults aged 26-60 years who responded "cool" and the percentage of adults aged 18-25 years who responded "cool"?

4 \%

8 \%

14 \%

16 \%

Approach

The percentage of 26-60 years who responded "cool" is:

\frac{\text{responded "cool"}}{26-60 \text{ years old}}

= \frac{124}{325}

\approx 38\%

The percentage of 18-25 years who responded "cool" is:

\frac{\text{responded "cool"}}{18-25 \text{ years old}}

= \frac{74}{340}

\approx 22\%

The difference is $38-22=\boxed{16}$ .