Q#87: School mascots
Suppose a student poll is taken across three classrooms to decide on a new school mascot. In classroom A, 50% of students support a penguin mascot, in classroom B, 60% of the students support the penguin mascot, and in classroom C, 35% of the students support the penguin mascot.
Of the total population of the three classrooms, 40% are members of classroom A, 25% are members of classroom B, and 35% are members of classroom C.
Given that a student supports the penguin mascot, what is the probability that they are a member of classroom B?
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ANSWER
In the realm of data science, understanding probability theory and applying Bayes’ Theorem are fundamental skills. We have seen it before, so let’s apply it straight from the formula itself.
According to Bayes’ Theorem, the probability that a student belongs to classroom B, given that they support the penguin mascot (P(B|Penguin)), can be calculated as follows:
P(B|Penguin) = P(Penguin|B) * P(B) / P(Penguin)
Where P(Penguin|B) the probability of supporting the penguin mascot given the student belongs to classroom B (given as 60%). P(B): Probability of a student belonging to classroom B (given as 25%). P(Penguin): Probability of supporting the penguin mascot (given as the overall percentage of students supporting the mascot, calculated as the sum of products of probabilities of supporting the mascot in each classroom and the probability of being in that classroom)
P(Penguin) = P(Penguin|A) * P(A) + P(Penguin|B) * P(B) + P(Penguin|C) * P(C) = 0.5 * 0.4 + 0.6 * 0.25 + 0.35 * 0.35 = 0.2 + 0.15 + 0.1225 = 0.4725
P(B|Penguin) = (0.6 * 0.25) / 0.4725 ≈ 0.318
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