Taking 50/50 as a prior indicates that you don't know the true prevalence of C. Note that here 0.9 is not a probability, but rather a degree of belief. In this

Taking 50/50 as a prior indicates that you don't know the true prevalence of C. Note that here 0.9 is not a probability, but rather a degree of belief. In this concrete example it tells you how much you should be worried upon observing R. If the prevalence of C is unknown (even if C is actually rare!), then given a positive R one should be worried a lot, which is exactly what 0.9 says. Also note the language change and its implications for policy making, etc: Instead of saying "there is [not enough] evidence that .." we say "given the observations and these assumptions we should [not] believe/expect that .."