Subscriptions to a particular magazine are classified as gift, previous renewal, direct mail, and subscription service. In January 8% of expiring subscriptions were gifts; 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) that 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?