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 WXXX 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:
40% listen to WXXX
40% listen to WYYY
20% 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?
(b) What fraction of the listeners will WXXX have after 3 months?
(c) What fraction of the listeners will WYYY have after 5 months?