2018 SRJC P2 Q12

Based on past statistical data of high speed train journey, there is a \(8\%\) chance that a passenger with reservation made will not show up. In order to maximise revenue, a high speed train company accepts more reservations than the passenger capacity of its trains.

1. State \(2\) assumptions needed such that the number of passengers who do not show up for a high speed train journey may be well modelled by a Binomial distribution.[2]

A train company operates a high speed train from Burong Lake to Huahin Cove which has a capacity of \(280\) passengers.

2. Find the probability that when \(300\) reservations are accepted, the high speed train journey is overbooked, i.e. there is not enough seats available for the passengers who show up.[2]
3. Find the maximum number of reservations that should be accepted in order to ensure that the probability of overbooking is less than \(1\%\).[3]

The high speed train operates once daily throughout the year and \(300\) reservations are accepted for each journey.

4. Find the probability that no high speed train journey is overbooked in a week.[2]
5. Two such journeys from Burong Lake to Huahin Cove with \(300\) reservations each are examined. If the total number of passengers who turned up for these two journeys is at most \(550\) passengers, find the probability that one of the journeys is overbooked by at most \(2\) passengers.[3]