I am not sure if this is advanced probability but it is a question from third year genetics? I have done a lot of statistics but my probability is very weak indeed and this question is absolutely doing my head in.

I'm just not sure if I have the right answer and if I do, if I got the answer the right way. Could someone please tell me the simplest way to work out a question like this?


For the diagram below

(a) calculate the probability that each of the letters in the final container are the same (i.e AA, BB, CC etc)

(b) derive a simple formula to calculate probabilities given these types of paths.

I am more interested in the answer to A, if you can explain B to me as well that would be wonderful but it is not necessary.

Here is the picture (click on thumbnail):

How I got my answer was I drew out all of the possibilities which would end up with CC or DD in the last bubble (as they are the only letters that you could get two of) and then drew out all the TOTAL possibilities (took so long) and then divided the two which was

4/16 = 1/4 = .25

If I am right, which I doubt it, Id like to know the mathematical way (non drawing) of working it out. Like, possibility of choosing a C or D in the first level, then multiply that by possibility of choosing again etc...I dont even know how to word it... if that makes sense?

Thank you so much to whoever can rearrange my brain when it comes to this.