## 17. Sociological Survey

It is known that in a certain group of people, $42\%$ have never skied, $58\%$ have never flown on an airplane, and $29\%$ have both skied and flown on an airplane. In which case do we have a higher chance: meeting someone who has skied among those who have never flown on an airplane, or meeting someone who has flown on an airplane among those who have already skied?
17. If $42 \%$ of the people in the considered group have never skied, then $58 \%$ have skied. Since $29 \%$ of the people have skied and flown on an airplane, it follows that $29 \%$ have skied but have not flown on an airplane.

Therefore, the first probability we are interested in, which is the ratio of the number of people who have skied and not flown on an airplane to the number of people who have never flown on an airplane, is $29 / 58 = 1 / 2$.

![](https://cdn.mathpix.com/cropped/2024_05_21_fe999c0fe2ad81fc5164g-109.jpg?height=409&width=596&top_left_y=772&top_left_x=730)

The second probability mentioned in the problem is the ratio of the number of people who have flown on an airplane and skied to the number of people who have skied; it is $29 / 58 = 1 / 2$.

Thus, both probabilities are equal to each other.