the potential for new clients to alter the total revenue received by his business. Each new client is assessed as either a Follower (F) or an Influencer (FC) with a particular probability. The consultant has traditionally found that Influencers increase the total revenue of his business with a probability of 0.85 (I) or decrease it with a probability of 0.05 (D). There is a 10 percent chance that they will not alter the revenue (N). On the other hand, there is a 25 percent chance that those classified as Followers will increase his revenue but a 30 percent chance they will decrease it. (a) Place this information in a tree diagram using the symbols F, FC, I, D, and N to represent a Follower, an Influencer, an increase in the consultant's revenue, a decrease in revenue and no change in revenue. (b) The digital marketing consultant is 95 percent certain that a po- tential client can be characterised as a social media Follower. What is the probability that client will not increase his revenue? (c) Calculate Pr(F | IC) for this case. (d) Show that F and I are not independent events. (e) The consultant's risk profile dictates he only mentors clients that have less than a 50% chance of not increasing his revenue. What level of certainty does the consultant require that a client is not a Follower boforo agroping to mentor thom?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Transcribed Image Text:3. A digital marketing consultant is using probability theory to assess the potential for new clients to alter the total revenue received by his business. Each new client is assessed as either a Follower (F) or an Influencer (FC) with a particular probability. The consultant has traditionally found that Influencers increase the total revenue of his business with a probability of 0.85 (I) or decrease it with a probability of 0.05 (D). There is a 10 percent chance that they will not alter the revenue (N). On the other hand, there is a 25 percent chance that those classified as Followers will increase his revenue but a 30 percent chance they will decrease it. (a) Place this information in a tree diagram using the symbols F, Fº, I, D, and N to represent a Follower, an Influencer, an increase in the consultant's revenue, a decrease in revenue and no change in revenue. (b) The digital marketing consultant is 95 percent certain that a po- tential client can be characterised as a social media Follower. What is the probability that client will not increase his revenue? (c) Calculate Pr(F | Iº) for this case. (d) Show that F and I are not independent events. (e) The consultant's risk profile dictates he only mentors clients that have less than a 50% chance of not increasing his revenue. What level of certainty does the consultant require that a client is not a Follower before agreeing to mentor them?

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