1-aN 1-a [1] It is well known that a finite geometric series for a # 1 can be expressed -1a- Consider a sample space, S, of outcomes wj, j = 1, 2, ..., N where p(w;+1) = 2 * p(w;) for all j, and let p = p(w). Thus, with a = 2, p(1+2 +2+...+ 2N-) = P(S). [a] What must the value of p equal in order for the probability of the sample space to equal 1? [b] Write the probability of the event A = U=1 @j Note: both [a] and [b] need to be expressed concisely using the finite geometric series result. =