Wxxx, WYYY, AND wzzz are three radio stations that compete for listeners. Each m

Question

Wxxx, WYYY, AND wzzz are three radio stations that compete for listeners. Each month some of the listeners switch from one station to another while some remain loyal to their current station. It has been found that each month 20% of the listeners of wox switch to wYYY 10% of the listeners of wxxx switch to wzzz 30% of the listeners of WYYY switch to wxxx 10% of the listeners of wYYY switch to wzzz 20% of the listeners of wzzz switch to wxxx 30% of the listeners of wzzz switch to wYYY Currently, the listening audience is divided as follows: 20% listen to wxxx 40% listen to wYYY 4096 listen to wzzz Use this information to answer the following questions. (Give your answers correct to three decimal places. Note that you are asked to give decimal values and not percentages. For example, you would need to enter 0.628 as opposed to 62.800%) (a) What fraction of the listeners will WZZZ have after 2 months? 0.204 (b) What fraction of the listeners will XXX have after 3 months? 0.04 (c) What fraction of the listeners will WYYY have after 5 months? 00265

Explanation / Answer

solution=

a) 0.4+0.1^2*0.2+0.1^2*0.4-(0.2^2*0.4+0.3^2*0.4) = 0.354

b) 0.2+0.2^3*0.4+0.3^3*0.4-(0.1^3*0.2) = 0.2138

C) 0.4+0.3^5*0.4-(0.1^5*0.4+0.3^5*0.4) = 0.39996

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