Airlines sometimes overbook flights (that is, they sell more tickets than there are seats on the plane). Suppose that for a plane with 50 seats, the airline has sold 55 tickets. Define the random variable X as the number of ticketed passengers who actually show up for the flight. The probability distribution function of X is shown in the table below.

x	45	46	47	48	49	50	51	52	53	54	55
p(x)	0.05	0.10	0.12	0.14	0.28	0.17	0.06	0.02	0.03	0.02	0.01

Question 1. What is the probability that the flight will accommodate all ticketed passengers who show up?

Question 2. Calculate E(X), the expected number of ticketed passengers who show up for the flight.

Question 3. If you are the first person on the standby list (which means you will be the first one to get on the plane if there are any seats available after all ticketed passengers have been accommodated), what is the probability that you will be able to take the flight?

Question 4. If you are the third person on the standby list, what is the probability that you will be able to take the flight?