Probability?

Subscriptions to a particular magazine are classified as gift, previous renewal, direct mail, and subscription service. In January 8% of expiring subscriptions were gift; 41%, previous renewal; 6%, direct mail; and 45%, subscription service. The percentages of renewals in these four categories were 81%, 79%, 60%, and 21%, respectively. In February of the same year 10% of expiring subscriptions were gift; 57%, previous renewal; 24%, direct mail; and 9%, subscription service. The percentages of renewals were 80%, 76%, 51%, and 14%, respectively.





a. Find the probability that a randomly chosen subscription expiring in January was renewed.





b. Find the probability that a randomly chosen subscription expiring in February was renewed.





c. Verify that the probability in part (b) is higher than that in part (a). Do you believe that the editors of this magazine should view the change from January to February as a positive or negative development?

Probability?
To find the probability of a randomly selected subscription is renewed in January or Febraury, take each of the four categories (gift, previous, direct, and service) renewal rates and multiply it by its percentage of the total. Then, add up the four percentages.





JAN


Gift = 8% * 81% = 6.48%


Previous = 41% * 79% = 32.39%


Direct = 6% * 60% = 3.6%


Service = 45% * 21% = 9.45%


TOTAL = 51.92%





FEB


Gift = 10% * 80% = 8%


Previous = 57% * 76% = 43.32%


Direct = 24% * 51% = 12.24%


Service = 9% * 14% = 1.26%


TOTAL = 64.82%





It is a negative development. While the total subscription rate improved in February, the renewal rate in each category went down.





Gift renewal went from 81% to 80%.


Previous renewal went from 79% to 76%


Direct renwewal went from 60% to 51%


Service renewal went from 21% to 14%