# Sketch a complete tree diagram

Question

Mega Electronics is producing smart watches. The company will start operating a night shift from 1st January 2018. Currently, there are 15 machinist employed by the company.
(a) If a night crew consists of 3 machinist, how many different crews are possible?
(b) If the machinist are ranked 1, 2, 3, …., 15 in order of competence, how many of these
crews found in (a) would have the best machinist?
(c) How many of the crews would have at least one of the 5 best machinists?
2. A survey at a petrol station shows that 45% of the customers use petrol RON95, 30% use petrol RON97 and 25% use diesel. Of those customers using petrol RON95, 70% fill up their vehicle tanks to full level. Of those customers using petrol RON97, 60% fill up their vehicle tanks to full level, whereas of those using diesel, 50% fill up their vehicle tanks to full level.
(a) Sketch a complete tree diagram to represent the above scenario.
(b) Solve the probability that a randomly selected customer fills up his/her vehicle tank to
full level.
(c) Given a randomly selected customer fills up his/her vehicle tank to full level, what is
the probability he/she uses petrol RON97.