1. A manufacturer of electric generators buys engines for its generators from three companies, \(R , S\) and \(T\).

Company \(R\) supplies 40\% of the engines. Company \(S\) supplies \(25 \%\) of the engines. The rest of the engines are supplied by company \(T\). It is known that \(2 \%\) of the engines supplied by company \(R\) are faulty, \(1 \%\) of the engines supplied by company \(S\) are faulty and \(2 \%\) of the engines supplied by company \(T\) are faulty. An engine is chosen at random.

1. Draw a tree diagram to show all the possible outcomes and the associated probabilities.
2. Calculate the probability that the engine is from company \(R\) and is not faulty.
3. Calculate the probability that the engine is faulty. Given that the engine is faulty,
4. find the probability that the engine did not come from company \(S\).