Flat screen TVs require high quality glass with very few flaws. A television manufacturer receives glass panels from two different suppliers. Let x and y denote the number of flaws in a randomly selected glass panel from the first and second suppliers, respectively. Suppose that the probability distributions for x and y are as follows. x 0 1 2 3 4
p(x) 0.4 0.3 0.2 0.1 0

y 0 1 2 3 4
p(y) 0.2 0.6 0.2 0 0

The mean values of both x and y are 1. However, the probability distribution for the second supplier is concentrated closer to the mean value than is the first supplier's distribution.

Required:
a. What is the probability that the airline can accommodate everyone who shows up for the flight?
b. What is the probability that not all passengers can be accommodated?
c. If you are trying to get a seat on such a flight and you are number 1 on the standby list, what is the probability that you will be able to take the flight? What if you are number 3?