noun
1
BAD : We are considering the possibility to do the job ourselves.
GOOD : We are considering the possibility of doing the job ourselves.
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possibility of ( doing ) sth : 'Is there any possibility of (getting) a refund?'
Compare: 'Is it possible to get a refund?'
2
BAD : My visit to Tokyo was a good possibility for me to learn some Japanese.
GOOD : My visit to Tokyo was a good opportunity to learn some Japanese.
BAD : A person who wants to go out to work should be given the possibility to do so.
GOOD : A person who wants to go out to work should be given the opportunity to do so.
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Use possibility when you are talking about something that may happen: 'There is also a possibility that the peacekeeping forces could themselves come under attack.'
To refer to a situation in which it is possible for someone to do something, use opportunity : 'The exchange scheme provides young people with the opportunity to visit a foreign country.'