Contrast this to the notion we have in probability theory, of an exact quantitative rational judgment. If 1% of women presenting for a routine screening have breast cancer, and 80% of women with breast cancer get positive mammographies, and 10% of women without breast cancer get false positives, what is the probability that a routinely screened woman with a positive mammography has breast cancer? 7.5%. You cannot say, "I believe she doesn't have breast cancer, because the experiment isn't definite enough." You cannot say, "I believe she has breast cancer, because it is wise to be pessimistic and that is what the only experiment so far seems to indicate." 7.5% is the rational estimate given this evidence, not 7.4% or 7.6%. The laws of probability are laws.

I try to do the math when you pose a problem. I'm pretty sure in this case the rational estimate is 7.4%. If 1000 women get tested, you expect 8 of those women to be true positives and 100 to be false positives. 8/108 is .074074... (ellipsis for repeating, I don't know how to do a superscripted bar in a comment here). I have no particular objections to rounding for ease of communication, and would ordinarily consider this sort of correction to be an unnecessary nitpick, but in this case, I'm objecting to the statement that 7.4% is not the correct rational estimate given the evidence, not the statement that 7.5% is. If you happen to read this comment, you might want to change that.