possibility-n; 3 Senses

Sense Number 1: a potential or prospective value

Commentary: POSSIBILITY[+quality][+value][+potential]
NOTE: assigns a potential value to an entity, implies a positive quality. Answers the question 'who or what has value'

The realtor suggested the house had great possibilities with a little work.
She erroneously perceived the student to have limited possibilities.

WordNet 3.0 Sense Numbers: 1

Sense Number 2: a measure of likelihood, the chance of something occurring

Commentary: POSSIBILITY[+quantity][+measure][+likelihood] Refers to the likelihood or chance of something. The answer is a measurement.

The weatherman says there is no possibility of rain tomorrow afternoon.
What's the possibility of moving the meeting to next Tuesday?

WordNet 3.0 Sense Numbers: 2

Sense Number 3: a hypothetical alternative, a possible state

Commentary: POSSIBILITY[+state][+hypothetical][+alternative]
NOTE: refers to a possible state of affairs, concrete or abstract The answer is a situation.

He proposed the possibility that the five theories might be unified into one.
One possibility is to have one-on-one negotiations with them.
The possibility of bankruptcy never entered his mind.

WordNet 3.0 Sense Numbers: 3, 4