1% of women at age forty who participate in routine screening have breast cancer. 80% of women with breast cancer will get positive mammographies. 9.6% of women without breast cancer will also get positive mammographies. A woman in this age group had a positive mammography in a routine screening. What is the probability that she actually has breast cancer?
It may seem like a simple math/statistics problem on the surface – and to be fair, it kinda is – but only 15% of medical professionals get the answer correct.
[PS this is not a riddle, no word-play here. This is a sort of a poll I’m taking on ILP. Please do not cheat, avoid looking around on the internet or on the answers in this thread, just use the information given and whatever math/statistics knowledge you have to figure out the answer.]