The probability that the passenger will be late for the train departure is 0.02. Find the probability

The probability that the passenger will be late for the train departure is 0.02. Find the probability that out of ten passengers who bought a train ticket, there will be at least two latecomers.

The probability of being late for the train: p = 0.02;
The probability of not being late for the train: q = 1 – p = 1 – 0.02 = 0.98;
The probability that there will be no latecomers:
P10 (0) = q ^ 10 = 0.98 ^ 10 = 0.817;
The probability that there will be 1 latecomer:
P10 (1) = C (10.1) * p ^ 1 * q ^ 9 = 10 * 0.02 ^ 1 * 0.98 ^ 9 = 0.167;
The probability that there will be 0 or 1 latecomers:
P10 (<2) = P10 (0) + P10 (1) = 0.817 + 0.167 = 0.984;
The probability of an opposite event such that there will be at least 2 latecomers:
P10 (> 1) = 1 – P10 (<2) = 1 – 0.984 = 0.016.
Answer: 0.016.