Poisson Distribution - Conditional Probability Question I have come across a question in my notes and I do not understand how to solve it. I have looked at the solutions and I still am unclear!
This is the question:

And this is the solution:

I really don't understand what the question is really asking - would anyone be able to explain to me with an example? I also don't understand what the implication of the conditional probability is: e.g. the prob of 1 goal being scored given that 1 or more goals have already been scored? But then that should be independent?
Sorry - again, I am very confused and any help would be much appreciated!

Conditional probability is a measure of a set (N==1) occupies upon the (N>=1) partition (rather than the whole unity, as it is for unconditional probability). Understanding this fact makes conditional probability much more intuitive.
In a physical sense, among all the cases one or more events of interest happened within a given time interval, 40% of the cases only contained one event.
Now, the question is, what was the average event rate per time interval (lambda)?
Next, Poisson is a discrete distribution, so we can calculate the probability of N being 1 using Poisson PMF (lambda ^ 1 * exp(-lambda) / 1!)
Probability of N>=1 is also easy to be calculated as 1 - PMF(0).
Calculating via 'trial and error' is of course not the best exercise they could think of but at least it's doable.
