Final answer:
The question asks for probabilities related to overbooked flights, given the chance a passenger misses a flight. The probabilities of interest, when 54 or 58 tickets are sold, require binomial probability calculations. The absence of the exact calculation in the question suggests the student should learn to apply the binomial formula themselves.
Step-by-step explanation:
Probability of an Overbooked Flight
The student's question revolves around the probability of overbooking flights. Consider the probability that a passenger misses their flight to be 0.0991. With a plane seating capacity of 52 passengers, we are to calculate the following probabilities based on ticket sales:
- Probability that 53 or 54 passengers show up when 54 tickets are sold.
- Probability that a passenger will have to be bumped if 58 tickets are sold.
Since these are similar to binomial probability problems, they could be solved by summing the individual probabilities of the number of passengers not showing up until we reach the number required that would result in an overbooked flight. The binomial probability formula is:
P(X=k) = (n choose k) * p^k * (1-p)^(n-k)
Where:
- n is the total number of tickets sold,
- k is the number of passengers showing up,
- p is the probability of a passenger not missing the flight (1-0.0991=0.9009).
Use this formula to calculate the required probabilities for each case. Normally, this would involve calculations for each case separately, requiring the use of a calculator or statistical software.