To find the probability that Mrs Lin sits directly behind a student and Mrs Brown sits in the front row, we can use the following approach:

There are 14 seats, and 12 passengers are seated randomly. We need to calculate the probability of the specific seating arrangement.

First, calculate the total number of ways to arrange 12 passengers in 14 seats: \(^{14}P_{12}\).

Next, calculate the favorable outcomes:

1. Choose 3 seats for Mrs Brown in the front row: 3 ways.
2. Choose 10 seats for Mrs Lin to sit directly behind a student: 10 ways.
3. Choose 5 students to sit in front of Mrs Lin: 5 ways.

The number of favorable outcomes is: \(3 \times 10 \times 5 \times ^{11}P_9\).

The probability is then given by: \(\frac{3 \times 10 \times 5 \times ^{11}P_9}{^{14}P_{12}}\).

Calculating this gives: \(\frac{150}{2184} = 0.0687\).