Mathematics

Mathematics

Problem

In a class of 40 students, 18 play cricket, 15 play football and 7 play both. Treating selection of a student at random as an experiment, decide whether the events AA: "the student plays cricket" and BB: "the student plays football" are independent.
Intuitive explanation

Two events are independent when knowing one happened doesn't change the probability of the other—mathematically, when P(A∩B)=P(A)⋅P(B)P(A \cap B) = P(A) \cdot P(B). Here you'll use a Venn diagram to find the actual probabilities from the given counts, then check if this multiplication rule holds. If it does, the events are independent; if not, they're dependent.

Intuitive explanation

Two events are independent when knowing one happened doesn't change the probability of the other—mathematically, when P(A∩B)=P(A)⋅P(B)P(A \cap B) = P(A) \cdot P(B). Here you'll use a Venn diagram to find the actual probabilities from the given counts, then check if this multiplication rule holds. If it does, the events are independent; if not, they're dependent.

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