Exercise 3
In Figure 1, the five circles in the network R represent five people linked together via the seven
communication lines shown in the picture as edges $e_1, e_2, ..., e_7$ (that is, we have a little social network).
We will assume that the reliability of each of the links is known; that is, that the probability that the link
is working is known. Furthermore, let's assume that the links are independent. As a convenient notation,
we denote by $p_i$, the probability that link $e_i$ is good.
In this exercise, you will calculate the reliability of communication between the two people represented
by the black nodes using the relevant rules of probability learned in class, chosen among the addition
rule, the product rule for independent events, and the complement rule.
Label events so equations can be used and show your work in detail.
Figure 1.