QUESTION TWO IN WITH A CHANCE 16 MARKS Problems involving probability are among the most challenging in the mathematical world but also the most practical. Can you answer those below QUESTION ONE (3 MARKS) One hundred people lineup to board an airplane. Each has a boarding pass with assigned seat. However, the first person to board has lost his boarding pass and takes a random seat. After that, each person takes the assigned seat if it is unoccupied, and one of unoccupied seats at random otherwise. What is the probability that the last person to board gets to sit in his assigned seat QUESTION TWO (5 MARKS) Mr. Smith works on the 13th floor of a 15 floor building. The only elevator moves continuously through floors 1, 2, . . . , 15, 14, . . . , 2, 1, 2, . . . , except that it stops on a floor on which the button has been pressed. Assume that time spent loading and unloading passengers is very small compared to the travelling time. Mr. Smith complains that at pm, when he wants to go home, the elevator almost always goes up when it stops on his floor. What is the explanation Now assume that the building has n elevators, which move independently. Compute the proportion of time the first elevator on Mr. Smith’s floor moves up.