Question

A local car dealership currently has 36 used GM, Food, and Toyota vehicles on the lot that are cars or turcks. Inventory shows the following: 26 vehicles are cars, 10 are trucks, 11 vehicles are GM's, 15 vehicles are Fords. Three vehicles are Toyota trucks and 14 vehicles are Ford cars. What is the probability that a randomly selected vehicle is either a Ford or a car

Answer 1

P (F or C) = 27/36= 0.75

Explanation:

There are 36 vehicles in all.

There are total 26 cars.

There are total Ford vehicles which are 15 in number out of which 14 are cars. The results can be summarized as follows.

Cars Trucks Total Vehicles

Ford 14 1 15

Toyota 7 3 10

Gm 5 6 11

Total 26 10 36

As the events are composite

The probability of randomly selecting vehicle is either a Ford or a car is given by P (F or C) = P(F) + P(c)- P(FC)

where P(F) is the probability of the Ford car and P (C) is the probability of the car.

P(F)= 15/ 36

P(C)= 26/36

P(FC)= 14/36

This is the additive rule applied for composite events.

P (F or C) = P(F) + P(c)- P(FC)

= 15/36 + 26/36- 14/36

= 27/36=0.75