The Sun's magnetic field now and then accelerates a gigantic amount of high velocity protons in different directions. Regardless of the types and causes, let's call it "proton storm" when it is dangerous enough to cause radiation acute sickness to astronauts outside of the useful natural protection of Earth's magnetic field and atmosphere.
What is the probability that a deep space mission gets hit by such a Solar proton storm? The Apollo missions all were lucky in this respect. But how lucky were they? As a benchmark, let's assume here the same radiation protection that the Apollo missions had, which I understand wasn't much at all.
What's the probability for a half-month Apollo type crew on the sunny side of the Moon being hit by an acutely unhealthy Solar proton storm?
What's the probability of a 26 months Hohmann conjunction mission to, and on, Mars having to experience such an event? If they did it the Apollo way in terms of radiation protection.
The further out from the Sun, the lower the impact, I suppose. Would it for example be a non-issue for humans at Saturn? Is there a neat probability distribution as a function of distance and time?