Markov Chain Transition Matrix Question

Ok, so my question is pretty simple, the question states:

A spider web is only big enough to hold 2 flies at a time. Assuming that the flies fly into the web independently:

-The probability that no flies will fly into her web on any given day is $0.5$.

-The probability that exactly one fly will fly into her web on any given day is $0.3$.

-The probability that two or more flies will fly into her web on any given day is $0.2$.

It also states that if a fly flies into the web when the web is full, it will bounce off and escape. Every morning the spider checks the web and will always eat a flies if there is one available, but can only eat 1 a day, leaving any left for the next day.

So, my transition matrix for this is:

$$M = \begin{bmatrix}0.5 & 0.3 & 0.2\\0.5 & 0.3 & 0.2\\0 & 0.5 & 0.5 \end{bmatrix}$$

The working after this is pretty simple, I'm just not sure if I've done the matrix correctly, any help is appreciated.

• I don't understand what the assumption that the flies fly into the web independently is doing there. You're already giving us the distribution of the number of flies that fly into the web per day, and it seems that that's all you're interested in -- why add an assumption about the independence of the flies? – joriki May 23 '16 at 11:35
• That's what the question said, I'm not entirely sure how that affects the question though. – L. Murphy May 23 '16 at 11:39
• If you copy questions from another source (and especially if you're not sure whether the question is posed correctly), please state the source. – joriki May 23 '16 at 11:47
• It's just a homework question, I didn't think that was too important. – L. Murphy May 23 '16 at 11:49
• Please see How to ask a good question?, and perhaps also (though slightly older) How to ask a homework question?. – joriki May 23 '16 at 11:52