Assume that for a certain stock, its price today is $50. Further assume that for each day,the stock price on the next day can either go up by $10 with probability 40% or go down by $10 with probability 60%.
Call today day 0, consider the events
A = (1st day's price is $40);
B = (2nd day's price is $50);
C = (the stock price goes up by $10 on the 2nd day).
(a) Is A independent of C?
(b) What is the probability that the 2nd day's stock price is $50 given that the 1st day's price is $60?
(c) What is P(B)?
(d) Is A independent of B?