I hate statistics...?

The first thing to realise (and probably the purpose of the question) is that the first nine months has no impact on the remainder of the year. So, the question is effectively asking for the probability of zero crashes in 3 months.
  
You have an average value, which is 2.5/12 crashes per month and that is all you need to look up or calculate the Poisson value for p(0) in one month. Then it is p(0)^3  for 3 consecutive months.

Alternatively, you could start with the average per three months, which is
2.5 x 0.25 and than for that average you should be able to look up p(0) directly and get the same answer.

Added:

Yahoo Answers removed the ability to comment on answers because they had degenerated into extensive insults and trolling on subjects like Trump, Creationism etc.

But yes to everything you said. A Poison distribution is the limit of a binomial distribution when the time interval of a trial tends to zero and the number of trials tends to infinity. For some reason I always think of it in terms of customers walking into a shop. There is some characteristic rate at which customers turn up, which is n per day or hour or minute but there are no individual trials like with tossing a coin. A customer could turn up at any time with equal probability and is independent of all other customers 

This is the story of Poisson distributions in my mind: 

For a small shop that isn't too busy you might consider that every minute is a trial and during that minute you either get one customer or not with probability p. Then you could use a binomial distribution to evaluate the probability of x customers in an hour or a day (on the basis that every minute is unaffected by every other minute).

But if you start getting two customers in the same minute you can't use this method (because success is one customer), so when the shop gets busier you might switch to each trial being one second and there is a new probability for each trial and more trials in an hour or day.

But for a department store there might be multiple doors and several customers entering per second, so to use the binomial distribution you might need to use the probability of a customer entering each hundredth of a second. 

And you can see where this is going. We have an average rate but in reality each instant is effectively a trial and there are infinitely many because in practice a customer can turn up at any time. So mathematically you take the equation for a binomial distribution and tweak it such that the number of trials tends to infinity and the average stays the same and that's what the Poisson distribution is - the limit of a binomial distribution. There is effectively a constant "infinitesimal instantaneous probability" of an event happening (event independence) but we characterise that probability as an average per large interval because it is meaningless and useless to actually have a value for an instantaneous probability.

Thanks @Dixon - i dont know why  Yahoo answers dont let you reply directly to submissioners.

So it looks like you can solve this in two ways.
If we define P( X = k)  by  p(x, lambda) , where X ~ poisson(x, lambda) ,
then we want p(0, 2.5* 1/12 ) ^3 if we are looking at a time interval of one month.
Alternatively we can look at a three month interval, p( 0, 2.5  * 3/12).

Just to clarify the first 9 months are irrelevant to the problem?

What if there was a crash in the first 9 months, and we want to know probability of 0 plane crash in the next 3 months. The answer would be the same.

It sounds like the poisson distribution is 'memoryless', same with flipping a coin. Probability of what happens in next toss does not depend on last toss.