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The task is to determine the probability that the first randomly selected song from the iPod is an 80s song. When dealing with probabilities, it's important to remember that they represent the likelihood of an event happening out of a total possible outcomes. Here, the different possible outcomes are the set categories of music on the iPod.

The iPod is filled with songs divided into three groups: songs you like, your sister's songs, and 80s songs. You've been given percentages for the first two groups:

• 60% for your favorite songs,
• 25% for your sister's songs.

To find the probability that an 80s song plays first, calculate the remaining percentage of the iPod's music that belongs to this category. Subtract the sum of the first two percentages from 100%: \[ 100\% - 60\% - 25\% = 15\% \].
This 15% represents the chances, or the probability in decimal form, of the first song being one of those 80s classics, equivalent to 0.15. This means there is a 15% chance of an 80s song being played next from the iPod.

Identifying the probability that a song picked by either you or your sister is played demands understanding the relationship between these individual probabilities. Because we are looking at two groups of songs, the songs you like and the ones chosen by your sister, you simply need to add the two probabilities together.

The events considered here are you picking a song you like, which is 60%, and picking a song your sister likes, which is 25%. Both probabilities can be summed to find the overall likelihood that a song from either child is played. Thus: \[ 60\% + 25\% = 85\% \].
This means there is an 85% probability, or 0.85 in decimal form, that the iPod will play a song that was picked by one of the kids during the first shuffle.

This method of finding probabilities by addition works perfectly in this case because choosing you or your sister's song are mutually exclusive events; they cannot occur simultaneously.

The concept of a complement in probability is used to determine the chance of an event not occurring, which can often simplify complex probability calculations. Here, we're calculating the likelihood that the iPod does not play a song you like.

The complement rule states that the probability of an event not occurring is 1 minus the probability of the event occurring. To apply this here, let's start with the probability of a song you like. If the songs you like make up 60% of the iPod, then the probability that a song you like will play is 0.60.

• The complement of this event, that is, a song not from your selection playing, is calculated as:

\[ 1 - 0.60 = 0.40 \].
Thus, there is a 40% chance, or 0.4 in decimal form, that the iPod will select a song that is not yours as the first song. This showcases how the complement rule often offers a more intuitive approach to solving what might seem like complex probability problems.