using past data, an airline believes that 8% of the people who make reservation for a particular flight will not appear. for this flight, the seating capacity is 300 passengers and the airline sells 315 tickets. what is the probability that everyone who shows up will have a seat?
To find the probability that everyone who shows up will have a seat, we need to consider the number of people who are likely to show up and the number of seats available.
Given that the airline believes 8% of people who make a reservation will not appear, we can assume that 92% will actually show up. However, the airline has sold 315 tickets for a flight with a seating capacity of 300 passengers.
To calculate the probability, we need to compare the number of people who may show up to the number of available seats. In this case, we have two scenarios:
1. If the number of people who show up is less than or equal to 300, everyone will have a seat.
2. If more than 300 people show up, not everyone will have a seat.
Let's calculate the probability for both scenarios.
Scenario 1:
The number of people who show up is less than or equal to 300. In this case, everyone will have a seat. Since 92% of people who make a reservation are likely to show up, the number of people who show up can be calculated as follows:
Number of people who show up = 92% of the number of tickets sold
Number of people who show up = 0.92 * 315
Number of people who show up ≈ 289.8 (rounded to the nearest whole number)
Since 289.8 is less than or equal to 300, everyone will have a seat.
Therefore, the probability in Scenario 1 is 100%.
Scenario 2:
The number of people who show up is more than 300. Since the seating capacity is 300 passengers, it means that not everyone will have a seat.
Therefore, the probability in Scenario 2 is 0%.
To find the overall probability, we need to consider both scenarios. Since Scenario 1 has a probability of 100% and Scenario 2 has a probability of 0%, the overall probability that everyone who shows up will have a seat is:
Overall probability = Probability of Scenario 1 + Probability of Scenario 2
Overall probability = 100% + 0%
Overall probability = 100%
So, the probability that everyone who shows up will have a seat is 100%.