6. On Figure 1: each of the ve connections can be open or closed independently of other connections. The probability to have a specic connection closed is p. (a) Compute the probability that there is a path of closed connections from A to C. [One possible solution: by inclusionexclusion. To keep track of what you are doing, it might actually be easier to denote the probability of each connection by a. different letter]. (b) Compute the conditional probability that the connection along the diagonal ED is closed given that there is a path of closed connections from A to C. 'Whatever answer you get in both parts (a) and (b): check that the result is a. function that is monotonically increasing from 0 when p = D to 1 when p = 1 (it might be easier to do it using a. computer algebra system).