The 200 students of a school were classified by sex and by whether they own a bicycle. Girls: owns 48, does not own 32. Boys: owns 72, does not own 48. Which statement about the events 'the student is a girl' and 'the student owns a bicycle' is correct?

Independence is a statement about PROPORTIONS, not about totals. Of the 80 girls, 48 own a bicycle, a rate of 48/80 = 0.6; of the 120 boys, 72 own one, a rate of 72/120 = 0.6; and overall 120 of 200 own one, again 0.6. Since knowing the student's sex does not change the chance of ownership, the two events are independent. The formal test agrees: P(girl and owns) = 48/200 = 0.24 while P(girl) × P(owns) = $0.4\times 0.6=0.24$. The counts 72 and 48 differ only because there are more boys in the school; comparing raw counts across groups of different sizes is the commonest error with a two-way table. The events are certainly not mutually exclusive — 48 students are girls AND own a bicycle, so the two can and do happen together, which is a different idea altogether from independence.