- In a factory, three machines, \(J , K\) and \(L\), are used to make biscuits.
Machine \(J\) makes \(25 \%\) of the biscuits.
Machine \(K\) makes \(45 \%\) of the biscuits.
The rest of the biscuits are made by machine \(L\).
It is known that \(2 \%\) of the biscuits made by machine \(J\) are broken, \(3 \%\) of the biscuits made by machine \(K\) are broken and 5\% of the biscuits made by machine \(L\) are broken.
- Draw a tree diagram to illustrate all the possible outcomes and associated probabilities.
A biscuit is selected at random.
- Calculate the probability that the biscuit is made by machine \(J\) and is not broken.
- Calculate the probability that the biscuit is broken.
- Given that the biscuit is broken, find the probability that it was not made by machine \(K\).