6 and 7 go together

6) Assume given an electrical network with 3 vertices's and four segments between those vertices's: (see black board) the segments a and b go in parallel from a to y, whilst d goes from y to 2. Finally e goes also from y to z. Each of the segments works independently form the others. Let A be the event that segment a works, let B be the event that segment b works,... Let pa be the probability that a works, hence pa = P(A). Let p, be equal to P(B),. .. We assume that pa; Ph, Pc, pa are all given to us. Let E be the event that electricity can flow from a to z. Calculate P(E) in terms of Pa, Ph, Pe and pa. 7) Same setting as in the previous problem. What is the (conditional) probability that segment a and b work, if we know that E holds (i.e. we know that electricity can flow from a to z