Question

Exercise 6. Consider a parking lot having 8 consecutive slots (meaning that the slots are one after the other). A blue car and a red car have parked uniformly at random. 1) Construa a finite probability space to model this experiment. 2) What is the probability that the first slot has been taken by a car? 3) What is the probability that the two cars have parked next to each other?

Answer 1

There are 8 consecutive parking slots and a blue & a red car have parked uniformly at random.

1) The all possible ways to park two cars at random into 8 slots = 8P2=8! /6! =56.

2) If the first slot is taken by a car, then the other car can park in any one of the 7 slots. The first slot can be chosen randomly by any one of the 2cars. So, all possible ways to do that is 2*7= 14 ways. Therefore the required probability = 14/56 = 1/4.

3) If two cars have parked next to each other, then if one car is parked at terminal position the other has only one dpace, otherwise for any of 6 places, the other car has 2 options. So the total number of options= 2*6+2*1=14. Therefore the required probability=14/56=1/4.