A ‣ Obligation 

You will be liable /ˈlaɪəbl/ for any damage when you rent a car. [obliged to pay; fml/ legalistic]
The company is obliged to give a refund if the tour is cancelled.
The bank robbers forced him at gunpoint to open the safe.
We had no choice/alternative but to sell our house; we owed the bank £100,000.
The death sentence is mandatory /ˈmændətəri/ for drug-smuggling in some countries. [automatic; there is no alternative)
Was sport compulsory/obligatory at your school? No, it was optional. [you can choose]
I am exempt from paying income tax as I'm a student. [free from obligation)
B ‣ Need 

This plant is in need of water. (more formal than 'needs/wants')
There's a need for more discussion on the matter. [we feel a need; fml]
There is a shortage of teachers. [there are not enough] .
She could not concentrate through lack of sleep. [she had none or not enough; fml]
A car is an absolute necessity if you live in the countryside and have no public transport. [something you must have] You just can't do without one. [survive or live without]
What are the requirements for a Master's course in English? [things you must do or need]
C ‣ Possibilities
I've been given an opportunity to work in Bonn. [a real chance]
Is there any chance/possibility you'll be free next week? (chance is less formal than possibility)
A rise in oil prices is inevitable as oil supplies run out across the world. [is certain to happen]
It is doubtful whether the economy will improve next year. [it may not improve]
It is probable that the next government will change the tax laws.
Most scientists believe that climate change is no longer just a possibility but is now an absolute certainty.
Common mistakes
The correct preposition after the noun need is for, not of. There is a need for more qualified teachers. (NOT There is a need of...)