In a city with 200,000 households, each household subscribes to exactly one of t
ID: 3107854 • Letter: I
Question
In a city with 200,000 households, each household subscribes to exactly one of the two local newspapers A and B, or else to none. A survey has determined the following:
80% of the households that have a subscription to newspaper A continue their subscription the following year and 20% subscribe to none.
50% of the households that have a subscription to newspaper B continue their subscription the following year, and 40% switch to newspaper A.
20% of the households that have neither subscription will subscribe to newspaper A the following year, and 10% subscribe to newspaper B.
At present, 50,000 households subscribe to newspaper A, 20,000 households subscribe to newspaper B, and 130,000 subscribe to neither.
In the questions below, assume that the number of households in the city remains constant.
1. [2 pts.] The Smiths currently have a subscription to newspaper B. How likely is it that they
will subscribe to neither newspaper two years from now?
2. [2 pts.] How many households will have subscription to newspaper B two years from now?
3. [1 pts.] Without lengthy calculation, explain whether the numbers of subscriptions to the
two newspapers will stabilize in the long run. (Use no more than two sentences.)
4. [5 pts.] In the long run, what percentage of households will subscribe to newspaper A
Explanation / Answer
1. There are two possible ways for this to happen one they switch to A then neither or they drop out now and to nothing. Switch to A .4 times the decision for neither .2 .2x.4=.08 Go neither .1 don't subscribe .7=.07 .07+.08=.15 2. Chances you got to B if you are at A .2 goes to neither .1 goes to B=.02 If you are at neither .1x.5=.05 If you are at B .5x.5+.1x.1=.26 .26x20,000+50,000x.02+130,000x.02=13800 3. I think no because A get's it's costumers from B but B get's it from noone so I think it'll be volitale because if B goes down A get's less costumers than B pops up again. 4. It will go to about 100,000 or 50% because if it's lower than the non subscribers it will go up but if it is greater than it will go down