What it means
可能性がある expresses that a stated event, condition, or outcome is possible. It presents the possibility somewhat objectively and is common in explanations, reports, analyses, and cautious claims. It follows a noun with の, a plain verb clause directly, an i-adjective directly, and a na-adjective with な. The polite counterpart is 可能性があります.
Usage note
可能性がある usually evaluates whether something is possible rather than simply expressing the speaker's immediate uncertainty. For a noun, の is required, while na-adjectives retain な before the expression. The polite form 可能性があります changes the register without changing the meaning.
How to use it
計画変更の可能性があります。
There is a possibility of a change to the plan.
その説明は不十分な可能性があります。
That explanation may be insufficient.
この薬は副作用が強い可能性があります。
There is a possibility that this medicine has severe side effects.
委員会は来週、結論を発表する可能性があります。
The committee may announce the conclusion next week.
計画変更の可能性がある。
There is a possibility of a change to the plan.
その説明は不十分な可能性がある。
That explanation may be insufficient.
この薬は副作用が強い可能性がある。
There is a possibility that this medicine has severe side effects.
委員会は来週、結論を発表する可能性がある。
The committee may announce the conclusion next week.