I am finding the question above really confusing, sketching the pdfs is fine, but I don't understand how the pdfs give us the likelihoods ie p(x|A) and p(x|B). From what I have understood the p(x) values are not probabilities, rather the areas between points on the pdf give use the probabilities.
Later in this question it asks for the probability that given a tree is 6m tall, what is the probability that it is a type A tree?
So this is asking for p(A|x), so we can use bayes theorm to get this with a p(x|A), p(A) and p(x)....
In the solution, they simply sub in the equation of the pdf ie 10-x/50 for p(x|A) into bayes theorm, and this contradicts my understanding that the pdf itself does not output probabilities, which the solution implies when using it in bayes theorm, as our p(x|A).