+1 to sogood's comment on the probability of being hit, it does not accumulate over time.
+2 (or is it 3 or more now?)
A coin doesn't become heavier on the tails side if you have tossed 3 heads in a row, but the long term probability tends toward a 50% chance of tossing tails (or heads). Each coin flip has a 50% chance of being tails, as it is equally weighted. It's like the chances of catastrophic flooding in Brisbane are 1 in 100 each year, and not 1 in every 100 years. (a few locals that went through the 1974 flood expressed dismay that the next one came in less than 100 years).
A cyclist can keep their chances of crashing low by making sure they are observant (as mentioned by human909) and assertive in road positioning (as mentioned by Rustychisel). However a cyclist is not like a coin with a fixed probability of something happening, but they can learn from experience to ride to decrease their chances of having a prang.
Overall the chances of a cyclist crashing are probably lower than the alternative exercise or transport (and likely lower than doing nothing instead of cycling, with the risk of sedentary lifestyle related heath risks), and they do not necessarily increase with time.