2024 EJC P2 Q5

A company sells consumer hobby drones, and they buy the rotor motor parts from two suppliers, AE Rotors and Brushless Inc. \({25\%}\) of the motors are from AE Rotors and the rest are from Brushless Inc. The probability that a randomly chosen motor supplied by AE Rotors is faulty is \(\frac{1}{20}\). The probability that a randomly chosen motor supplied by Brushless Inc is faulty is \(q\).

1. Complete the tree diagram below to illustrate the possibilities for a randomly chosen motor. You should use the following notations for the events:

   \(A\) for the motor is supplied by AE Rotors.                      \(B\) for the motor is supplied by Brushless Inc.

   \(F\) for the motor is faulty, and                                         \(\quad\,{F}'\) for its complement, i.e. the motor is not faulty.

   [1]

It is known that the probability that a randomly picked motor that is faulty is supplied by Brushless Inc is \(\frac{3}{8}\).

2. Use the above information to set up an equation involving \(q\), and hence find the value of \(q\).[2]
3. Three motors are randomly picked. Find the probability that all of them are supplied by AE Rotors and exactly one of them is faulty.[2]