Villages a b c and d are connected by overhead telephone

Question

Villages A , B , C and D are connected by overhead telephone lines joining AB , AC , BC , BD and CD . As a result of severe gales, there is a probability p (the same for each link) that any particular link is broken.

1. Show that the probability that a call can be made from A to B is

          1 - p ² - 2 p ³ + 3 p ⁴ - p ⁵ .

2. Show that the probability that a call can be made from D to A is

        1 - 2 p ² - 2 p ³ + 5 p ⁴ - 2 p ⁵ .