Hello everyone,
I am new to this forum and I'm here because I'm stuck on a probability question that I was working on in preparation of an upcoming test.
Problem:
A parking lot has 16 spaces in a row. Each of the twelve cars took one parking space, and their drivers chose spaces at random from among the available spaces. After that a truck arrived and it requires 2 adjacent spaces to park. What is the probability that the truck will be able to park?
I couldn't quite figure out how to mathematically take into account the adjacent parking spaces. I started with 16!/12! which is the number of combinations that the 12 cars can occupy the 16 spaces. Afterwards, I resorted to counting the number of configurations for which 2 adjacent spaces could exist but that got me nowhere. My approach now is perhaps to find the probability of the complement (the chance that the truck cannot park at all) but again that would mean the 4 empty spaces cannot be adjacent and I don't know how to account for that.
The answer is 17/28.
Thank you all in advance!
I am new to this forum and I'm here because I'm stuck on a probability question that I was working on in preparation of an upcoming test.
Problem:
A parking lot has 16 spaces in a row. Each of the twelve cars took one parking space, and their drivers chose spaces at random from among the available spaces. After that a truck arrived and it requires 2 adjacent spaces to park. What is the probability that the truck will be able to park?
I couldn't quite figure out how to mathematically take into account the adjacent parking spaces. I started with 16!/12! which is the number of combinations that the 12 cars can occupy the 16 spaces. Afterwards, I resorted to counting the number of configurations for which 2 adjacent spaces could exist but that got me nowhere. My approach now is perhaps to find the probability of the complement (the chance that the truck cannot park at all) but again that would mean the 4 empty spaces cannot be adjacent and I don't know how to account for that.
The answer is 17/28.
Thank you all in advance!