Question

suppose there are 100 passengers boarding a flight. one of the passengers loses their ticket before boarding and sits on a random seat which is not the one assigned to them. what is the probability that last passenger sit on their assigned

Answer 1

The probability that the last passenger sits on their assigned seat is 1/2.

Step-by-step explanation:

To calculate the probability that the last passenger sits on their assigned seat, we can use the concept of permutations. Let's consider the two possible scenarios:

1. If the first passenger, who lost their ticket, sits on their assigned seat, there will be no issues with the seating arrangement and the last passenger will also sit on their assigned seat. So, the probability in this case is 1/2.
2. If the first passenger sits on a random seat other than their assigned seat, it sets off a chain reaction where subsequent passengers may also sit on random seats. In this case, the last passenger will not be able to sit on their assigned seat. The probability in this case is also 1/2.

Considering these two scenarios are equally likely, we can calculate the probability by taking the average of the two probabilities: (1/2 + 1/2) / 2 = 1/2. Therefore, the probability that the last passenger sits on their assigned seat is 1/2.