Instruction: Use the principle of inclusion-exclusion to solve this problem.
Context: This question assesses the candidate's understanding of the principle of inclusion-exclusion in the context of set theory and probability.
To answer this question, we need to apply the principle of inclusion and exclusion to accurately calculate the total number of people who like either chocolate or vanilla ice cream or both. The principle of inclusion and exclusion helps us avoid double-counting those who like both flavors.
First, let's sum up the individual counts: there are 120 people who like chocolate and 80 who like vanilla. If we naively added these numbers, we would get 200. However, this approach mistakenly counts the people who like both flavors twice. We know that 60 people enjoy both flavors, so we must subtract this overlapping group to correct our overcount.
By applying the formula for the principle of inclusion and exclusion, we find the correct total by adding the number of chocolate lovers to the number of vanilla lovers and then subtracting the number of people who like both flavors: (120 + 80 - 60 = 140).
This tells us that 140 out of the 200 surveyed people like either chocolate or vanilla ice cream. To find the probability that a randomly chosen person from this survey likes either chocolate or vanilla ice cream, we divide the number of people who like either by the total number of people surveyed: (140 / 200). Simplifying this fraction gives us (7 / 10) or 0.7.
Therefore, the probability that a person chosen at random from this survey likes either chocolate or vanilla ice cream is 0.7, or 70%. This calculation demonstrates not only the application of fundamental probability concepts but also showcases the analytical thinking essential in fields such as data science and analytics. It's an illustration of how mathematical principles are pivotal in deriving insights from data, a core aspect of our role that enables us to make informed decisions and provide valuable recommendations.
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