Please help answer and show work please

1. A sample space consists of the following simple events: S = w1 x1 yl z1 w2 x2 yz z2 w3 x3 y3 z3 Let the events on this sample space be defined as follows: A: (observe a number > 2} B: observe z a. List the simple events in events A and B and find P(A) and P(B). A = P A = B =1. P B = b. List the simple events in A' and B' and find P(A') and P(B'). A' = 1. P ( A ' ) = B' = 1. P (B' ) = C. List the simple events in AUB and AB and find P(AUB ) and P(AB ). AUB = . P (A UB) = AB = P AB) = d. Are A and B mutually exclusive? WHY? e. Are A and B independent? WHY