2024 TJC H1 Q8

A school has a large number of students. A student is randomly chosen from the school.

Let \(G\text{ be the event that the student is a girl, and}\) \(S\text{ be the event that the student is shortsighted.}\)

It is given \(\mathrm{P}(G)=0.62\), \(\mathrm{P}(S|G')=0.2\) and \(\mathrm{P}(G|S')=0.392\).

1. Describe, in the context of the question, the event \(G'\cap S'\).[1]
2. Find the probability that the randomly chosen student is either a girl or is shortsighted or both.[3]
3. Find the probability that the randomly chosen student is a girl with shortsightedness.[3]
4. Determine whether \(G\) and \(S\) are independent events.[1]