Question

A. Suppose you have three possible outcomes following the occurrence of an event. These are {no harm, some harm, a lot of harm}. Are elements of this set of outcomes mutually exclusive? Statistically independent? Can they be both? Why or why not?

B. Suppose you have three dimensions of harm of concern - confidentiality, integrity, and availability. Following the occurrence of an event, you may or may not suffer a breach of confidentiality, integrity or availability. Whether you suffer loss of confidentiality is statistically independent from loss of integrity or loss of availability. Furthermore, suppose the outcome on each dimension is binary - loss or not. How many mutually exclusive, collectively exhaustive outcome possibilities do you have? List them.

Answer 1

(A) we have given element of outcomes are (no harm, some harm, a lot of harm) we will find is they mutully exclusive or statistically independent. (I) mutually exclusive events are event that cannot occur at same time and probability of occuring events together is zero. Here, no harm, some harm, and a lot of harm are events which are cannot be occure at the same time. This three event will not happen together. Hence elements of this set of outcomes are mutually exclusive. (II) statistical independent : events are said to be statistically independent if occurence of one event does not affects probability of occurence of other events. Here probability of occurence of event no harm does not change probability of occurence of event so harm and event a lot of harm. So they are statistically independent. (III) hence given elements of set of outcomes are both mutually exclusive and statistically independent. Because they satisfied condition of both mutually exlusive event. And statistically independent events. (B) we have given three dimensions of harm of concern which are, confidentiality, integrity, availability. (l) you suffer loss of confidentiality is not statistically independent from loss of integrity or loss of availablity. Because confidentiality, integrity, availability are dependent variable. They affects on each other so that probability of occurence of loss of confidentiality affects on probability of loss of integrity and availability. Hency they are not statistically independent. ( II) we have given outcome of each dimension is binary loss or not . Hence let event A= confidentiality={ loss, not loss} ; let event B=integrity = {loss, not loss} let event C=availability={loss, not loss} . Event are said to be mutually exclusive event. If event cannot happen simultaneously. If intersection of event A, B, C is zero. Then they mutully exclusive. Here intersection of A, B, C ={loss,not loss}which is is not equal to zero. Hence this are not mutully exclusive event. Hence number of mutually exclusive event is 0. (III) collectively exhastive events are event if at least one of event must occure. Or set of event covers entire sample space. {Loss confidentiality, not loss confidentiality, loss integrity, not loss integrity, loss availability, not loss availability} is collectively exhastive outcomes because they encompasses entire range of possible outcomes.