2024 EJC H1 Q8

A company has two teams, Team \(A\) and Team \(B\). There are \(800\) workers in Team \(A\) and \(600\) workers in Team \(B\). Each worker works in either the manufacturing, logistics or accounting department and the numbers of each are summarised in the table.

A worker is chosen at random from the company.

1. Find the probability the worker does not work in the manufacturing department.[1]
2. Find the probability that the worker is from Team \(A\) or works in the logistics department.[1]
3. Determine whether or not the events 'the worker works in the accounting department' and 'the worker is from Team \(A\)' are independent.[3]

On another occasion, \(3\) of the workers are chosen at random, without replacement.

4. Find the probability that exactly \(2\) are from Team \(B\).[2]