[14 marks] A car rental company rents two types of vehicles: electric cars (EVs) and diesels (D). Each vehicle is classified by size, either small (S), medium (M) or large (L). The company inventory consists of a total of 100 vehicles. There are 50 EV's, 5 of which are large. There are 50 small cars, 10 of which are diesels and there are 10 medium sized diesels. Choosing a car at random from the company and using obvious notation so that the probability of choosing a small EV is written P(EV, S) find: (A table would be useful for this) (a) P(EV,S) (b) The probability of choosing a small EV or a large diesel. (c) The probability of choosing a small EV given that the vehicle is not large. (d) The probability of choosing anything except a small EV. (e) Show that type and size are either independent or dependent quantities in the vehicle inventory.