The probability that a person takes a holiday in their own country is 0.65. For a group of n people, the probability that all take a holiday in their own country is given by:

\((0.65)^n < 0.002\)

Taking logarithms on both sides, we have:

\(n \cdot \log(0.65) < \log(0.002)\)

Solving for n, we get:

\(n > \frac{\log(0.002)}{\log(0.65)}\)

Calculating the right-hand side:

\(\log(0.002) \approx -2.69897\)

\(\log(0.65) \approx -0.18709\)

Thus:

\(n > \frac{-2.69897}{-0.18709} \approx 14.43\)

Since n must be an integer, the smallest possible value of n is 15.