Problem 5: Construct a 3 period tree diagram and associated probability distribution:

The inputs are :

Problem 4: (Zippo Airlines) Suppose that in flight, airplanes engines fail with probability "q", constant and independent from engine to engine. A two engine plane makes a successful flight if at least one of the two engines work. A four engine plane makes a successful flight if 2 or 3 or 4 engines work. a. Using algebra and concept of Binomial Experiment, find the probability that a 2 engine airplane makes a successful flight. Express your answer as a formula totally in terms of "q". Remember p= 1-q. Repeat the exercise for four engines plane. b. For what value of "q" are these airplanes equally safe? For what values are the 2 engines planes safer? For what values are the 4 engines planes safer? (You should get a 4th degree equation that has nice factors). Problem 5: Construct a 3 period tree diagram and associated probability distribution: The inputs are: S = 100 the stock price 6 = 0.4 the volatility per annum t = 0.25 the time to expiration (3 months) n = 3 the number of periods r = 0.12 the per annum rate of return compounded monthly. You must compute u, d, mr, p, q, Now from the above, compute C100, the value now of the 100 call as per : C100 = ( rr ) " E(C100) where E is the expected value of the call option at the expiration