Real-world independence interpretation

A question is this type if and only if it presents a real-world scenario (e.g., exam results, student activities) and asks whether achieving one outcome is independent of achieving another based on given data.

2 questions

CAIE S1 2018 June Q2
2 In a group of students, \(\frac { 3 } { 4 }\) are male. The proportion of male students who like their curry hot is \(\frac { 3 } { 5 }\) and the proportion of female students who like their curry hot is \(\frac { 4 } { 5 }\). One student is chosen at random.
  1. Find the probability that the student chosen is either female, or likes their curry hot, or is both female and likes their curry hot.
  2. Showing your working, determine whether the events 'the student chosen is male' and 'the student chosen likes their curry hot' are independent.
OCR MEI Paper 2 2018 June Q12
12 You must show detailed reasoning in this question. In the summer of 2017 in England a large number of candidates sat GCSE examinations in both mathematics and English. 56\% of these candidates achieved at least level 4 in mathematics and \(80 \%\) of these candidates achieved at least level 4 in English. 14\% of these candidates did not achieve at least level 4 in either mathematics or English. Determine whether achieving level 4 or above in English and achieving level 4 or above in mathematics were independent events.