4 A manufacturer produces three models of washing machine: basic, standard and deluxe. An analysis of warranty records shows that \(25 \%\) of faults are on basic machines, \(60 \%\) are on standard machines and 15\% are on deluxe machines. For basic machines, 30\% of faults reported during the warranty period are electrical, \(50 \%\) are mechanical and \(20 \%\) are water-related. For standard machines, 40\% of faults reported during the warranty period are electrical, \(45 \%\) are mechanical and 15\% are water-related. For deluxe machines, \(55 \%\) of faults reported during the warranty period are electrical, \(35 \%\) are mechanical and \(10 \%\) are water-related.

1. Draw a tree diagram to represent the above information.
2. Hence, or otherwise, determine the probability that a fault reported during the warranty period:
   1. is electrical;
   2. is on a deluxe machine, given that it is electrical.
3. A random sample of 10 electrical faults reported during the warranty period is selected. Calculate the probability that exactly 4 of them are on deluxe machines.