Firstly, are you sure the needle was used by a patient who has HIV?
Assuming yes:
Actually, contrary to the answers I see here so far, the possibility is not zero – it happened many times before. A nurse in the United States in the 1980s got infected by HIV when she accidentally pricked herself on a needle.
See the full story below.
Nurse who contracted HIV with jab sheds anonymity
But, the chance of this happening is very low.
According to the article, as of 2011, there were only 13 such documented cases in the USA.
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