There isn't really much to add but since the site insists at least 30 chars body, I am asking again : If something happens to 1 in 100 persons, is the chance of that person being you 50/50?
Being that person with a 50/50 chance means, that almost every second person in a group will be concerned because you have a chance of 50% being the one or 50% not being the one. The probability you are looking for is
If we think of any disease you will be affected with the probability of 1% and with probability 99% you will be healthy.
An example for the 50/50 chance would be a model with balls and bins. Assume we have one bin and $n$ blue and $n$ red balls in there. You are allowed to take one ball without explicitly looking which color it has - the probability of it being blue/red will be both $50\%$ because $n$ out of $2n$ balls have the same property (here the color). If you want to repeat this experiment keep in mind to put the ball back, otherwise you would get other probabilities!