Final answer:
The problem presented involves calculating the complementary probability of not hearing a song from a favorite group on a playlist in the field of high school Mathematics, specifically probability.
Step-by-step explanation:
The question involves calculating the probability of an event not happening in a given scenario, which clearly falls into the Mathematics subject area. Specifically, it fits probability and combinatorics which is often taught at the high school level. In the context of a shuffled playlist with 889 songs where 127 are by a student's favorite group, the task is to figure out the likelihood of not hearing any song by that favorite group during a random play of a song from the playlist.
The first step is to determine the total number of songs that are not by the favorite group: 889 - 127 = 762. When a single song is played at random, the chances of it being by the favorite group are 127/889. Thus, the probability of it not being by the favorite group is the complementary probability, which is 762/889.
To solve the problem, we calculate:
P(not hearing favorite group) = Number of songs not by favorite group / Total number of songs
P(not hearing favorite group) = 762 / 889
After performing the division, we obtain the exact probability. This understanding of probability is an important mathematical concept that has real-world applications, such as the mentioned poll about music preferences where the chance of participants downloading music weekly could be evaluated.