A sample space contains seven sample points and eventsA,B, andC,as shown in the Venn diagram. The probabilities of the sample points areP(1)=0.01,P(2)=0.15,P(3)=0.22,P4=0.04,P(5)=0.18,P(6)=0.25 andP(7)=0.15.

Which pairs of events, if any, are mutually exclusive? Why?

1. Which pairs of events, if any, are independent? Why?

1. FindPAB by adding the probabilities of the sample points and then using the additive rule. Verify that the answers agree.

1. The journal Networks periodically publishes studies on the reliability of flow networks. For example,Networks(September 2007) provided mobile ad hoc and sensor networks applications. Consider a similar network with an activity called "Arc". The probability distribution of the capacityxfor the Arc is provided in the following table.

x	0	1	2	3
p(x)	.15	.30	.15	.40

1. Verify that the properties of discrete probability distributions are satisfied for the Arc capacity distribution.

1. Find the probability that the capacity will exceed 1.

1. Compute for the Arc and interpret the results.

1. Compute for the Arc and interpret the results.