Identifying joint/conditional probability from question I am trying to solve a basic probability question. This problem is an example of the law of total probability. Here is the problem with its solution.


I interpreted the first line of the question as $P(C \cap M) = 0.07$ and $P(C \cap F) = 0.004$.
But from the solution, it appears the first line meant conditional probability, not a joint probability.
My question is, how am I supposed to understand that the statement meant conditional and not joint probability? Also, is the question poorly written?
 A: The sentence "7% of men ... are colorblind." means "Among men, 7% are colorblind." or in symbols, $P(C|M) = 0.07.$ By contrast, $P(M\cap C) = 3.43\%$ ought to go into English as "In the US population 3.43% are colorblind men."
However, too many imprecise and/or innumerate writers are not careful to distinguish between $|$ and $\cap.$ For example, in accounts of medical screening tests the terminology "false positive" has come to be used about equally often as either "Positive test and not infected: in the population" or "Positive test among those not infected", conflating probabilities $P(+\cap D^c)$ and $P(+|D^c).$
It has come to the point that "false positive" has become either meaningless, or a puzzle to be solved before reading further. In my own writing, I have decided to use "false positive" and "false negative" only
if accompanied by a correct mathematical expression in the same immediate field of view.
Note: For a long time, Wikipedia had a lengthy, excellent, and technically meticulous article on screening tests; but it got replaced by a more popularized, and less precise, article. In sequence, various
different pages have followed under the same header. (I have not checked the current
version before writing this.)
