"Chance of [gerund]" vs. "chance at [gerund]"

Which is correct?

• If you tell me the cause, I will have a better chance at fixing the problem.
• If you tell me the cause, I will have a better chance of fixing the problem.

A quick Google search for the two phrases returns a nearly equal number of results. So, perhaps both are correct.

However, there are some scenarios where it seems "chance of" is the only correct option. For example,

The chances of dying in an airplane crash are nearly 100%.

Using "chances at dying" doesn't seem right in the above statement.

Are there any general usage guidelines for this?

Solution 1:

Chance of and chance at mean different things. The first refers to likelihood, the second to opportunity.